Shun-Chen Niu - Academia.edu (original) (raw)

Papers by Shun-Chen Niu

Research paper thumbnail of North-Holland Analyzing household brand switching

Abstract: In a recent study, Kahn, Morrison and Wright showed that for exponentially distributed ... more Abstract: In a recent study, Kahn, Morrison and Wright showed that for exponentially distributed interpurchase times (of individuals), the household choice process approaches a zero-order process as the number of individuals in the household increases, even though the purchasing behavior of each individual is first order. We show that their result holds for any arbitrary interpurchase-time distribution that has a density over some interval. Thus, additional support is provided for their conclusion that the empirically observed zero-order choice behavior at the household level may not convey much information about individuals ' choice behavior. We also derive a general formula that determines exactly the degree of dependence between two successive household purchases for any given family size and (well-behaved) interpurchase-time distribution.

Research paper thumbnail of Representing Workloads in Gi/G/I Queues Through the Preemptive-Resume

We give in this paper a detailed sample-average analysis of GI/G/1 queues with the preemptive-res... more We give in this paper a detailed sample-average analysis of GI/G/1 queues with the preemptive-resume LIFO (last-in-first-out) queue discipline: we study the long-run "state" behavior of the system by averaging over arrival epochs, departure epochs, as well as time, and obtain relations that express the resulting averages in terms of basic characteristics within busy cycles. These relations, together with the fact that the preemptive-resume LIFO queue discipline is work-conserving, imply new representations for both "actual" and "virtual" delays in standard GI/G/1 queues with the FIFO (first-in-first-out) queue discipline. The arguments by which our results are obtained unveil the underlying structural "explanations" for many classical and somewhat mysterious results relating to queue lengths and/or delays in standard GI/G/1 queues, including the well-known Bene~'s formula for the delay distribution in M/G/1. We also discuss how to extend o...

Research paper thumbnail of Comparing alternating renewal processes

Naval Research Logistics Quarterly, 1981

Sufficient conditions are given for stochastic comparison of two alternating renewal processes ba... more Sufficient conditions are given for stochastic comparison of two alternating renewal processes based on the concept of uniformization. The result is used to compare component and system performance processes in maintained reliability systems.

Research paper thumbnail of On queues with dependent interarrival and service times

Naval Research Logistics Quarterly, 1981

An M / C / l queueing svsleni IS siudied iii which l l i e w r v i c c tinic required bv ;I cusio... more An M / C / l queueing svsleni IS siudied iii which l l i e w r v i c c tinic required bv ;I cusionicr is dependent o n the intcriirriviil l i m e beiwccn this arrival and i1i;ii ol' his predecessor Assuming ihc iwo variables are ";issocialed," we prove 1h;ii [lie e x p e c~c d delav i n [his svsicni is less than or equal io i h i i i 01' Li convcniion;il M / G / I queue This coiicltision h:is heen verified vi;i siniul~itioti hv Miichell .ind I'LiuIsnn 191 l o r ii spcci;iI class 01' dcpendcni M /. I I / I queue 'Their model is ii spccial ciisc 01' ihc one we consider here. We iilso siudv iinoihcr iiiodilietl G//C/ I qucue. where i h c arriviil proccs\ ;ind/or t h e set-vice process ;ire individu;illv ";issnci,iied "

Research paper thumbnail of Optimality of (s, S) Inventory Policies under Renewal Demand and General Cost Structures

Production and Operations Management, 2017

W e study a single-stage, continuous-time inventory model where unit-sized demands arrive accordi... more W e study a single-stage, continuous-time inventory model where unit-sized demands arrive according to a renewal process and show that an (s, S) policy is optimal under minimal assumptions on the ordering/procurement and holding/backorder cost functions. To our knowledge, the derivation of almost all existing (s, S)-optimality results for stochastic inventory models assume that the ordering cost is composed of a fixed setup cost and a proportional variable cost; in contrast, our formulation allows virtually any reasonable ordering-cost structure. Thus, our paper demonstrates that (s, S)-optimality actually holds in an important, primitive stochastic setting for all other practically interesting ordering cost structures such as well-known quantity discount schemes (e.g., all-units, incremental and truckload), multiple setup costs, supplier-imposed size constraints (e.g., batch-ordering and minimum-order-quantity), arbitrary increasing and concave cost, as well as any variants of these. It is noteworthy that our proof only relies on elementary arguments.

Research paper thumbnail of Optimality of ( s , S ) policies in EOQ models with general cost structures

International Journal of Production Economics, 2017

The classical economic-order-quantity (EOQ) model is at the heart of supply chain optimization an... more The classical economic-order-quantity (EOQ) model is at the heart of supply chain optimization and the theory of inventories. We study an extension of the original EOQ model that permits a minimal set of assumptions on the ordering/procurement and holding/backorder cost, and establish necessary and sufficient conditions for the existence of an optimal policy of the (s, S) type. Our work lends theoretical credibility to the practice of using (s, S) policies for virtually any cost structure of practical interest. Our proof is constructive and elementary, in the sense that it is based on first principles that do not rely on advanced mathematical machinery. We also prove that an optimal policy, not necessarily of the (s, S) type, always exists within our general EOQ framework.

Research paper thumbnail of Bounds and Comparisons for Some Queueing Systems

Abstract : Bounds and comparisons for various performance measures in tandem queueing systems and... more Abstract : Bounds and comparisons for various performance measures in tandem queueing systems and loss systems are studied. Using a definition of variability of random variables, it is proven that for a tandem queueing system with n stations in series, where each station can have either one server with an arbitrary service distribution or a number of constant servers in parallel, the expected total waiting time in system of every customer decreases as the variability of interarrival and service distributions decreases. A new sufficient condition for customer average delay to be smaller (larger) than time average delay in single server queues is also given.

Research paper thumbnail of A Stochastic Model of Household Brand Switching Behavior

Research paper thumbnail of Representing workloads in GI/G/1 queues through the preemptive-resume LIFO queue discipline

Queueing Systems, 1988

We give in this paper a detailed sample-average analysis of GI/G/1 queues with the preemptive-res... more We give in this paper a detailed sample-average analysis of GI/G/1 queues with the preemptive-resume LIFO (last-in-first-out) queue discipline: We study the long-run "state" behavior of the system by averaging over arrival epochs, departure epochs, as well as time, and obtain relations that express the resulting averages in terms of basic characteristics within busy cycles. These relations, together with the fact that the preemptive-resume LIFO queue discipline is work-conserving, imply new representations for both "actual" and "virtual" delays in standard GI/G/1 queues with the FIFO (first-in-first-out) queue discipline. The arguments by which our results are obtained unveil the underlying structural "explanations" for many classical and somewhat mysterious results relating to queue lengths and/or delays in standard GI/G/1 queues, including the well-known Beneš's formula for the delay distribution in M/G/1. We also discuss how to extend our results to settings more general than GI/G/1.

Research paper thumbnail of Setups in polling models: does it make sense to set up if no work is waiting?

Journal of Applied Probability, 1999

We compare two versions of a symmetric two-queue polling model with switchover times and setup ti... more We compare two versions of a symmetric two-queue polling model with switchover times and setup times. The SI version has State-Independent setups, according to which the server sets up at the polled queue whether or not work is waiting there; and the SD version has State-Dependent setups, according to which the server sets up only when work is waiting at the polled queue. Naive intuition would lead one to believe that the SD version should perform better than the SI version. We characterize the difference in the expected waiting times of these two versions, and we uncover some surprising facts. In particular, we show that, regardless of the server utilization or the service-time distribution, the SD version performs (i) the same as, (ii) worse than, or (iii) better than its SI counterpart if the switchover and setup times are, respectively, (i) both constants, (ii) variable (i.e. non-deterministic) and constant, or (iii) constant and variable. Only (iii) is consistent with naive int...

Research paper thumbnail of Inventory and Shipment Policies for the Online Movie DVD Rental Industry

SSRN Electronic Journal, 2014

ABSTRACT The online movie rental industry in the United States has been growing at a rapid pace i... more ABSTRACT The online movie rental industry in the United States has been growing at a rapid pace in the past decade. Netflix and Blockbuster are prime examples of companies with a large subscriber base. For online rentals, two standard delivery methods are employed by these companies: streaming and DVD-by-mail service. While the industry is clearly undergoing a transition into streaming service, the majority of subscribers continue to prefer the more traditional DVD-by-mail service. This is due in part to the high bandwidth requirement of streaming and availability of the movies. In this paper, we will study the problem of how to efficiently manage DVD-by-mail service. An essential task in the solution of our problem is a proper understanding of subscriber demand. We will first develop a demand formulation based on data from Blockbuster. This formulation is then used to construct a nonlinear mathematical program for making the following decisions for the rental companies: (i) the initial order quantity of a new movie (DVD) title and (ii) the shipment sizes of the title for every period (i.e., day) after its release. Based on the structure of this mathematical program, we develop a policy that is shown to be potentially optimal through extensive computational experiments. The policy is simple, easy-to-understand, and easily implementable in practice.

Research paper thumbnail of IEEE 802.11 DCF performance evaluation using one-dimensional discrete time chains

2006 IEEE 63rd Vehicular Technology Conference

Previously proposed analytical studies for IEEE 802.11 Distributed Coordination Function model th... more Previously proposed analytical studies for IEEE 802.11 Distributed Coordination Function model the behavior of a wireless station operating under saturation conditions as a twodimensional discrete time Markov chain. In this document, we show that the two-dimensional chain can be partitioned into two one-dimensional chains. Such a partitioning not only simplifies the analysis, but also significantly reduces the number of state variables.

Research paper thumbnail of A duality relation for busy cycles inGI/G/1 queues

Queueing Systems, 1991

Using a generalization of the classical ballot theorem, Niu and Cooper [7] established a duality ... more Using a generalization of the classical ballot theorem, Niu and Cooper [7] established a duality relation between the joint distribution of several variables associated with the busy cycle in M/G/1 (with a modified first service) and the corresponding joint distribution of several related variables in its dual GI/M/1. In this note, we generalize this duality relation to GI/G/1 queues with modified first services; this clarifies the original result, and shows that the generalized ballot theorem is superfluous for the duality relation.

Research paper thumbnail of Relating polling models with zero and nonzero switchover times

Queueing Systems, 1995

We consider a system of N queues served by a single server in cyclic order. Each queue has its ow... more We consider a system of N queues served by a single server in cyclic order. Each queue has its own distinct Poisson arrival stream and its own distinct general service-time distribution (asymmetric queues); and each queue has its own distinct distribution of switchover time (the time required for the server to travel from that queue to the next). We consider two versions of this classical polling model: In the first, which we refer to as the zeroswitchover-times model, it is assumed that all switchover times are zero and the server stops traveling whenever the system becomes empty. In the second, which we refer to as the nonzero-switchover-times model, it is assumed that the sum of all switchover times in a cycle is nonzero and the server does not stop traveling when the system is empty. After providing a new analysis for the zero-switchover-times model, we obtain, for a host of service disciplines, transform results that completely characterize the relationship between the waiting times in these two, operationally-different, polling models. These results can be used to derive simple relations that express (all) waiting-time moments in the nonzeroswitchover-times model in terms of those in the zero-switchover-times model. Our results, therefore, generalize corresponding results for the expected waiting times obtained recently by Fuhrmann [8] and Cooper, Niu, and Srinivasan [4].

Research paper thumbnail of A Sales Forecast Model for Short-Life-Cycle Products: New Releases at Blockbuster

Production and Operations Management, 2012

W e develop, in this article, a sales model for movie and game products at Blockbuster. The model... more W e develop, in this article, a sales model for movie and game products at Blockbuster. The model assumes that there are three sales components: the first is from consumers who have already committed to purchasing (or renting) a product (e.g., based on promotion of, or exposure to, the product prior to its launch); the second comes from consumers who are potential buyers of the product; and the third comes from either a networking effect on closely tied (as in a social group) potential buyers from previous buyers (in the case of movie rental and all retail products) or re-rents (in the case of game rental). In addition, we explicitly formulate into our model dynamic interactions between these sales components, both within and across sales periods. This important feature is motivated by realism, and it significantly contributes to the accuracy of our model. The model is thoroughly tested against sales data for rental and retail products from Blockbuster. Our empirical results show that the model offers excellent fit to actual sales activity. We also demonstrate that the model is capable of delivering reasonable sales forecasts based solely on environmental data (e.g., theatrical sales, studio, genre, MPAA ratings, etc.) and actual first-period sales. Accurate sales forecasts can lead to significant cost savings. In particular, it can improve the retail operations at Blockbuster by determining appropriate order quantities of products, which is critical in effective inventory management (i.e., it can reduce the extent of over-stocking and under-stocking). While our model is developed specifically for product sales at Blockbuster, we believe that with context-dependent modifications, our modeling approach could also provide a reasonable basis for the study of sales for other short-life-cycle products.

Research paper thumbnail of The Waiting-Time Distribution for the GI/G/1 Queue under the D-Policy

Probability in the Engineering and Informational Sciences, 1992

We study a generalization of the GI/G/l queue in which the server is turned off at the end of eac... more We study a generalization of the GI/G/l queue in which the server is turned off at the end of each busy period and is reactivated only when the sum of the service times of all waiting customers exceeds a given threshold of size D. Using the concept of a “randomly selected” arriving customer, we obtain as our main result a relation that expresses the waiting-time distribution of customers in this model in terms of characteristics associated with a corresponding standard GI/G/1 queue, obtained by setting D = 0. If either the arrival process is Poisson or the service times are exponentially distributed, then this representation of the waiting-time distribution can be specialized to yield explicit, transform-free formulas; we also derive, in both of these cases, the expected customer waiting times. Our results are potentially useful, for example, for studying optimization models in which the threshold D can be controlled.

Research paper thumbnail of A Piecewise-Diffusion Model of New-Product Demands

Operations Research, 2006

The Bass Model (BM) is a widely-used framework in marketing for the study of new-product sales gr... more The Bass Model (BM) is a widely-used framework in marketing for the study of new-product sales growth. Its usefulness as a demand model has also been recognized in production, inventory, and capacity-planning settings. The BM postulates that the cumulative number of adopters of a new product in a large population approximately follows a deterministic trajectory whose growth rate is governed by two parameters that capture (i) an individual consumer's intrinsic interest in the product, and (ii) a positive force of influence on other consumers from existing adopters. A finite-population pure-birth-process (re)formulation of the BM, called the Stochastic Bass Model (SBM), was proposed recently by the author in a previous paper, and it was shown that if the size of the population in the SBM is taken to infinity, then the SBM and the BM agree (in probability) in the limit. Thus, the SBM “expands” the BM in the sense that for any given population size, it is a well-defined model. In th...

Research paper thumbnail of Inequalities between Arrival Averages and Time Averages in Stochastic Processes Arising from Queueing Theory

Operations Research, 1984

A common scenario in stochastic models, especially in queueing theory, is that an arrival countin... more A common scenario in stochastic models, especially in queueing theory, is that an arrival counting process both observes and interacts with another continuous time stochastic process. In the case of Poisson arrivals, Wolff (Wolff, R. W. 1982. Poisson arrivals see time averages. Opns. Res. 30 223–231.) recently proved that the proportion of arrivals finding the process in some state is equal to the proportion of time it spends there under a lack of anticipation assumption. Inspired by Wolff's approach, in this paper we study the related interesting question of when do we have inequalities between these proportions. We establish two-sided inequalities under the following three assumptions: (i) the interarrival time distributions are of type NBUE or NWUE, (ii) the process being observed have monotone sample paths between arrival epochs, and (iii) the state of the process does not depend on future jumps of the arrival process. These assumptions are typically true in all standard que...

Research paper thumbnail of A Single Server Queueing Loss Model with Heterogeneous Arrival and Service

Operations Research, 1980

A heterogeneous arrival and service single server queueing loss model is analyzed. The arrival pr... more A heterogeneous arrival and service single server queueing loss model is analyzed. The arrival process of customers is assumed to be a nonstationary Poisson process with an intensity function whose evolution is governed by a two-state continuous time Markov chain. Different service distributions for different types of customers are allowed. The explicit loss formula for the model considered is obtained. In a special case, it is shown that as the arrival process becomes more regular the loss decreases. For single server loss systems with renewal arrivals, counterexamples are given to show that regularity of arrival and service distributions do not work to good effect in general. Two sufficient conditions for it to be true are given.

Research paper thumbnail of A Decomposition Theorem for Polling Models: The Switchover Times are Effectively Additive

Operations Research, 1996

... We argue that the zero-switchover-times model is the more fundamental model: the mean waiting... more ... We argue that the zero-switchover-times model is the more fundamental model: the mean waitingtimes in the nonzero-switchover-times model decompose (reminiscent of vacation models) into a sum of two terms, one being a simple function of the sum of the mean switchover ...

Research paper thumbnail of North-Holland Analyzing household brand switching

Abstract: In a recent study, Kahn, Morrison and Wright showed that for exponentially distributed ... more Abstract: In a recent study, Kahn, Morrison and Wright showed that for exponentially distributed interpurchase times (of individuals), the household choice process approaches a zero-order process as the number of individuals in the household increases, even though the purchasing behavior of each individual is first order. We show that their result holds for any arbitrary interpurchase-time distribution that has a density over some interval. Thus, additional support is provided for their conclusion that the empirically observed zero-order choice behavior at the household level may not convey much information about individuals ' choice behavior. We also derive a general formula that determines exactly the degree of dependence between two successive household purchases for any given family size and (well-behaved) interpurchase-time distribution.

Research paper thumbnail of Representing Workloads in Gi/G/I Queues Through the Preemptive-Resume

We give in this paper a detailed sample-average analysis of GI/G/1 queues with the preemptive-res... more We give in this paper a detailed sample-average analysis of GI/G/1 queues with the preemptive-resume LIFO (last-in-first-out) queue discipline: we study the long-run "state" behavior of the system by averaging over arrival epochs, departure epochs, as well as time, and obtain relations that express the resulting averages in terms of basic characteristics within busy cycles. These relations, together with the fact that the preemptive-resume LIFO queue discipline is work-conserving, imply new representations for both "actual" and "virtual" delays in standard GI/G/1 queues with the FIFO (first-in-first-out) queue discipline. The arguments by which our results are obtained unveil the underlying structural "explanations" for many classical and somewhat mysterious results relating to queue lengths and/or delays in standard GI/G/1 queues, including the well-known Bene~'s formula for the delay distribution in M/G/1. We also discuss how to extend o...

Research paper thumbnail of Comparing alternating renewal processes

Naval Research Logistics Quarterly, 1981

Sufficient conditions are given for stochastic comparison of two alternating renewal processes ba... more Sufficient conditions are given for stochastic comparison of two alternating renewal processes based on the concept of uniformization. The result is used to compare component and system performance processes in maintained reliability systems.

Research paper thumbnail of On queues with dependent interarrival and service times

Naval Research Logistics Quarterly, 1981

An M / C / l queueing svsleni IS siudied iii which l l i e w r v i c c tinic required bv ;I cusio... more An M / C / l queueing svsleni IS siudied iii which l l i e w r v i c c tinic required bv ;I cusionicr is dependent o n the intcriirriviil l i m e beiwccn this arrival and i1i;ii ol' his predecessor Assuming ihc iwo variables are ";issocialed," we prove 1h;ii [lie e x p e c~c d delav i n [his svsicni is less than or equal io i h i i i 01' Li convcniion;il M / G / I queue This coiicltision h:is heen verified vi;i siniul~itioti hv Miichell .ind I'LiuIsnn 191 l o r ii spcci;iI class 01' dcpendcni M /. I I / I queue 'Their model is ii spccial ciisc 01' ihc one we consider here. We iilso siudv iinoihcr iiiodilietl G//C/ I qucue. where i h c arriviil proccs\ ;ind/or t h e set-vice process ;ire individu;illv ";issnci,iied "

Research paper thumbnail of Optimality of (s, S) Inventory Policies under Renewal Demand and General Cost Structures

Production and Operations Management, 2017

W e study a single-stage, continuous-time inventory model where unit-sized demands arrive accordi... more W e study a single-stage, continuous-time inventory model where unit-sized demands arrive according to a renewal process and show that an (s, S) policy is optimal under minimal assumptions on the ordering/procurement and holding/backorder cost functions. To our knowledge, the derivation of almost all existing (s, S)-optimality results for stochastic inventory models assume that the ordering cost is composed of a fixed setup cost and a proportional variable cost; in contrast, our formulation allows virtually any reasonable ordering-cost structure. Thus, our paper demonstrates that (s, S)-optimality actually holds in an important, primitive stochastic setting for all other practically interesting ordering cost structures such as well-known quantity discount schemes (e.g., all-units, incremental and truckload), multiple setup costs, supplier-imposed size constraints (e.g., batch-ordering and minimum-order-quantity), arbitrary increasing and concave cost, as well as any variants of these. It is noteworthy that our proof only relies on elementary arguments.

Research paper thumbnail of Optimality of ( s , S ) policies in EOQ models with general cost structures

International Journal of Production Economics, 2017

The classical economic-order-quantity (EOQ) model is at the heart of supply chain optimization an... more The classical economic-order-quantity (EOQ) model is at the heart of supply chain optimization and the theory of inventories. We study an extension of the original EOQ model that permits a minimal set of assumptions on the ordering/procurement and holding/backorder cost, and establish necessary and sufficient conditions for the existence of an optimal policy of the (s, S) type. Our work lends theoretical credibility to the practice of using (s, S) policies for virtually any cost structure of practical interest. Our proof is constructive and elementary, in the sense that it is based on first principles that do not rely on advanced mathematical machinery. We also prove that an optimal policy, not necessarily of the (s, S) type, always exists within our general EOQ framework.

Research paper thumbnail of Bounds and Comparisons for Some Queueing Systems

Abstract : Bounds and comparisons for various performance measures in tandem queueing systems and... more Abstract : Bounds and comparisons for various performance measures in tandem queueing systems and loss systems are studied. Using a definition of variability of random variables, it is proven that for a tandem queueing system with n stations in series, where each station can have either one server with an arbitrary service distribution or a number of constant servers in parallel, the expected total waiting time in system of every customer decreases as the variability of interarrival and service distributions decreases. A new sufficient condition for customer average delay to be smaller (larger) than time average delay in single server queues is also given.

Research paper thumbnail of A Stochastic Model of Household Brand Switching Behavior

Research paper thumbnail of Representing workloads in GI/G/1 queues through the preemptive-resume LIFO queue discipline

Queueing Systems, 1988

We give in this paper a detailed sample-average analysis of GI/G/1 queues with the preemptive-res... more We give in this paper a detailed sample-average analysis of GI/G/1 queues with the preemptive-resume LIFO (last-in-first-out) queue discipline: We study the long-run "state" behavior of the system by averaging over arrival epochs, departure epochs, as well as time, and obtain relations that express the resulting averages in terms of basic characteristics within busy cycles. These relations, together with the fact that the preemptive-resume LIFO queue discipline is work-conserving, imply new representations for both "actual" and "virtual" delays in standard GI/G/1 queues with the FIFO (first-in-first-out) queue discipline. The arguments by which our results are obtained unveil the underlying structural "explanations" for many classical and somewhat mysterious results relating to queue lengths and/or delays in standard GI/G/1 queues, including the well-known Beneš's formula for the delay distribution in M/G/1. We also discuss how to extend our results to settings more general than GI/G/1.

Research paper thumbnail of Setups in polling models: does it make sense to set up if no work is waiting?

Journal of Applied Probability, 1999

We compare two versions of a symmetric two-queue polling model with switchover times and setup ti... more We compare two versions of a symmetric two-queue polling model with switchover times and setup times. The SI version has State-Independent setups, according to which the server sets up at the polled queue whether or not work is waiting there; and the SD version has State-Dependent setups, according to which the server sets up only when work is waiting at the polled queue. Naive intuition would lead one to believe that the SD version should perform better than the SI version. We characterize the difference in the expected waiting times of these two versions, and we uncover some surprising facts. In particular, we show that, regardless of the server utilization or the service-time distribution, the SD version performs (i) the same as, (ii) worse than, or (iii) better than its SI counterpart if the switchover and setup times are, respectively, (i) both constants, (ii) variable (i.e. non-deterministic) and constant, or (iii) constant and variable. Only (iii) is consistent with naive int...

Research paper thumbnail of Inventory and Shipment Policies for the Online Movie DVD Rental Industry

SSRN Electronic Journal, 2014

ABSTRACT The online movie rental industry in the United States has been growing at a rapid pace i... more ABSTRACT The online movie rental industry in the United States has been growing at a rapid pace in the past decade. Netflix and Blockbuster are prime examples of companies with a large subscriber base. For online rentals, two standard delivery methods are employed by these companies: streaming and DVD-by-mail service. While the industry is clearly undergoing a transition into streaming service, the majority of subscribers continue to prefer the more traditional DVD-by-mail service. This is due in part to the high bandwidth requirement of streaming and availability of the movies. In this paper, we will study the problem of how to efficiently manage DVD-by-mail service. An essential task in the solution of our problem is a proper understanding of subscriber demand. We will first develop a demand formulation based on data from Blockbuster. This formulation is then used to construct a nonlinear mathematical program for making the following decisions for the rental companies: (i) the initial order quantity of a new movie (DVD) title and (ii) the shipment sizes of the title for every period (i.e., day) after its release. Based on the structure of this mathematical program, we develop a policy that is shown to be potentially optimal through extensive computational experiments. The policy is simple, easy-to-understand, and easily implementable in practice.

Research paper thumbnail of IEEE 802.11 DCF performance evaluation using one-dimensional discrete time chains

2006 IEEE 63rd Vehicular Technology Conference

Previously proposed analytical studies for IEEE 802.11 Distributed Coordination Function model th... more Previously proposed analytical studies for IEEE 802.11 Distributed Coordination Function model the behavior of a wireless station operating under saturation conditions as a twodimensional discrete time Markov chain. In this document, we show that the two-dimensional chain can be partitioned into two one-dimensional chains. Such a partitioning not only simplifies the analysis, but also significantly reduces the number of state variables.

Research paper thumbnail of A duality relation for busy cycles inGI/G/1 queues

Queueing Systems, 1991

Using a generalization of the classical ballot theorem, Niu and Cooper [7] established a duality ... more Using a generalization of the classical ballot theorem, Niu and Cooper [7] established a duality relation between the joint distribution of several variables associated with the busy cycle in M/G/1 (with a modified first service) and the corresponding joint distribution of several related variables in its dual GI/M/1. In this note, we generalize this duality relation to GI/G/1 queues with modified first services; this clarifies the original result, and shows that the generalized ballot theorem is superfluous for the duality relation.

Research paper thumbnail of Relating polling models with zero and nonzero switchover times

Queueing Systems, 1995

We consider a system of N queues served by a single server in cyclic order. Each queue has its ow... more We consider a system of N queues served by a single server in cyclic order. Each queue has its own distinct Poisson arrival stream and its own distinct general service-time distribution (asymmetric queues); and each queue has its own distinct distribution of switchover time (the time required for the server to travel from that queue to the next). We consider two versions of this classical polling model: In the first, which we refer to as the zeroswitchover-times model, it is assumed that all switchover times are zero and the server stops traveling whenever the system becomes empty. In the second, which we refer to as the nonzero-switchover-times model, it is assumed that the sum of all switchover times in a cycle is nonzero and the server does not stop traveling when the system is empty. After providing a new analysis for the zero-switchover-times model, we obtain, for a host of service disciplines, transform results that completely characterize the relationship between the waiting times in these two, operationally-different, polling models. These results can be used to derive simple relations that express (all) waiting-time moments in the nonzeroswitchover-times model in terms of those in the zero-switchover-times model. Our results, therefore, generalize corresponding results for the expected waiting times obtained recently by Fuhrmann [8] and Cooper, Niu, and Srinivasan [4].

Research paper thumbnail of A Sales Forecast Model for Short-Life-Cycle Products: New Releases at Blockbuster

Production and Operations Management, 2012

W e develop, in this article, a sales model for movie and game products at Blockbuster. The model... more W e develop, in this article, a sales model for movie and game products at Blockbuster. The model assumes that there are three sales components: the first is from consumers who have already committed to purchasing (or renting) a product (e.g., based on promotion of, or exposure to, the product prior to its launch); the second comes from consumers who are potential buyers of the product; and the third comes from either a networking effect on closely tied (as in a social group) potential buyers from previous buyers (in the case of movie rental and all retail products) or re-rents (in the case of game rental). In addition, we explicitly formulate into our model dynamic interactions between these sales components, both within and across sales periods. This important feature is motivated by realism, and it significantly contributes to the accuracy of our model. The model is thoroughly tested against sales data for rental and retail products from Blockbuster. Our empirical results show that the model offers excellent fit to actual sales activity. We also demonstrate that the model is capable of delivering reasonable sales forecasts based solely on environmental data (e.g., theatrical sales, studio, genre, MPAA ratings, etc.) and actual first-period sales. Accurate sales forecasts can lead to significant cost savings. In particular, it can improve the retail operations at Blockbuster by determining appropriate order quantities of products, which is critical in effective inventory management (i.e., it can reduce the extent of over-stocking and under-stocking). While our model is developed specifically for product sales at Blockbuster, we believe that with context-dependent modifications, our modeling approach could also provide a reasonable basis for the study of sales for other short-life-cycle products.

Research paper thumbnail of The Waiting-Time Distribution for the GI/G/1 Queue under the D-Policy

Probability in the Engineering and Informational Sciences, 1992

We study a generalization of the GI/G/l queue in which the server is turned off at the end of eac... more We study a generalization of the GI/G/l queue in which the server is turned off at the end of each busy period and is reactivated only when the sum of the service times of all waiting customers exceeds a given threshold of size D. Using the concept of a “randomly selected” arriving customer, we obtain as our main result a relation that expresses the waiting-time distribution of customers in this model in terms of characteristics associated with a corresponding standard GI/G/1 queue, obtained by setting D = 0. If either the arrival process is Poisson or the service times are exponentially distributed, then this representation of the waiting-time distribution can be specialized to yield explicit, transform-free formulas; we also derive, in both of these cases, the expected customer waiting times. Our results are potentially useful, for example, for studying optimization models in which the threshold D can be controlled.

Research paper thumbnail of A Piecewise-Diffusion Model of New-Product Demands

Operations Research, 2006

The Bass Model (BM) is a widely-used framework in marketing for the study of new-product sales gr... more The Bass Model (BM) is a widely-used framework in marketing for the study of new-product sales growth. Its usefulness as a demand model has also been recognized in production, inventory, and capacity-planning settings. The BM postulates that the cumulative number of adopters of a new product in a large population approximately follows a deterministic trajectory whose growth rate is governed by two parameters that capture (i) an individual consumer's intrinsic interest in the product, and (ii) a positive force of influence on other consumers from existing adopters. A finite-population pure-birth-process (re)formulation of the BM, called the Stochastic Bass Model (SBM), was proposed recently by the author in a previous paper, and it was shown that if the size of the population in the SBM is taken to infinity, then the SBM and the BM agree (in probability) in the limit. Thus, the SBM “expands” the BM in the sense that for any given population size, it is a well-defined model. In th...

Research paper thumbnail of Inequalities between Arrival Averages and Time Averages in Stochastic Processes Arising from Queueing Theory

Operations Research, 1984

A common scenario in stochastic models, especially in queueing theory, is that an arrival countin... more A common scenario in stochastic models, especially in queueing theory, is that an arrival counting process both observes and interacts with another continuous time stochastic process. In the case of Poisson arrivals, Wolff (Wolff, R. W. 1982. Poisson arrivals see time averages. Opns. Res. 30 223–231.) recently proved that the proportion of arrivals finding the process in some state is equal to the proportion of time it spends there under a lack of anticipation assumption. Inspired by Wolff's approach, in this paper we study the related interesting question of when do we have inequalities between these proportions. We establish two-sided inequalities under the following three assumptions: (i) the interarrival time distributions are of type NBUE or NWUE, (ii) the process being observed have monotone sample paths between arrival epochs, and (iii) the state of the process does not depend on future jumps of the arrival process. These assumptions are typically true in all standard que...

Research paper thumbnail of A Single Server Queueing Loss Model with Heterogeneous Arrival and Service

Operations Research, 1980

A heterogeneous arrival and service single server queueing loss model is analyzed. The arrival pr... more A heterogeneous arrival and service single server queueing loss model is analyzed. The arrival process of customers is assumed to be a nonstationary Poisson process with an intensity function whose evolution is governed by a two-state continuous time Markov chain. Different service distributions for different types of customers are allowed. The explicit loss formula for the model considered is obtained. In a special case, it is shown that as the arrival process becomes more regular the loss decreases. For single server loss systems with renewal arrivals, counterexamples are given to show that regularity of arrival and service distributions do not work to good effect in general. Two sufficient conditions for it to be true are given.

Research paper thumbnail of A Decomposition Theorem for Polling Models: The Switchover Times are Effectively Additive

Operations Research, 1996

... We argue that the zero-switchover-times model is the more fundamental model: the mean waiting... more ... We argue that the zero-switchover-times model is the more fundamental model: the mean waitingtimes in the nonzero-switchover-times model decompose (reminiscent of vacation models) into a sum of two terms, one being a simple function of the sum of the mean switchover ...