Priority Pricing in Queues with a Continuous Distribution of Customer Valuations (CMU-CS-13-109) (original) (raw)
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Speed is an increasingly important determinant of which suppliers will be given customers' business and is defined as the time between when an order is placed by the customer and when the product is delivered, or as the amount of time customers must wait before they receive their desired service. In either case, the speed a customer experiences can be enhanced by giving priority to that particular customer. Such a prioritization scheme will necessarily reduce the speed experienced by lower-priority customers, but this can lead to a better outcome when different customers place different values on speed. We model a single resource (e.g., a manufacturer) that processes jobs from customers who have heterogeneous waiting costs. We analyze the price that maximizes priority revenue for the resource owner (i.e., supplier, manufacturer) under different assumptions regarding customer behavior. We discover that a revenue-maximizing supplier facing self-interested customers (i.e., those that independently minimize their own expected costs) charges a price that also minimizes the expected total delay costs across all customers and that this outcome does not result when customers coordinate to submit priority orders at a level that seeks to minimize their aggregate costs of priority fees and delays. Thus, the customers are better off collectively (as is the supplier) when the supplier and customers act independently in their own best interests. Finally, as the number of priority classes increases, both the priority revenues and the overall customer delay costs improve, but at a decreasing rate.
2016
We consider the pricing/lead-time menu design problem for a monopoly service where time-sensitive cus-tomers have demand on multiple occasions. Customers differ in their demand rates and valuations per use. We compare a model where the demand rate is the private information of the buyers to a model where the firm has full information. The model assumes that customers queue for a finite-capacity service under a general pricing structure. Customers choose a plan from the menu to maximize their expected utility. In contrast to previous work, we assume customers do not differ in their waiting cost. Yet we show that in the private information case prioritizing customers may be optimal as a result of demand rate heterogeneity. We provide necessary and sufficient conditions for this result. In particular, we show that for intermediate capacity, more frequent-use customers that hold a lower marginal value per use should be prioritized. Fur-ther, less frequent-use customers may receive a con...
Optimal incentive-compatible pricing for M/G/1 queues
Operations Research Letters, 2003
This paper extends previous research on congested service facilities to generalized service distributions, a significant extension given the limitations of exponential distributions for networked computer job modeling. Building on the framework first presented in Mendelson and Whang (1990), we present fundamental theorems for non-priority M/G/1 queues, nonpreemptive M/G/1 queues, and preemptive-resume M/G/1 queues. For non-priority M/G/1 queues and nonpreemptive M/G/1 queues, these theorems establish optimal assignment rules and incentivecompatible pricing schemes. For preemptive-resume M/G/1 queues, we prove that the total delay cost is less than the total delay cost of nonpreemptive M/G/1 if service times are heterogeneous with decreasing failure rates. This result supports the traditional delay cost to service time ( i i c v
Wait Time Based Pricing for Queues with Customer-Chosen Service Times
SSRN Electronic Journal, 2020
This paper studies a pricing problem for a single-server queue where customers arrive according to a Poisson process. For each arriving customer, the service provider announces a price rate and a system wait time, and the customer decides whether to join the queue, and, if so, the duration of the service time. The objective is to maximize either the long-run average revenue or social welfare. We formulate this problem as a continuous-time control model whose optimality conditions involve solving a set of delay differential equations. We develop an innovative method to obtain the optimal control policy, whose structure reveals interesting insights. The optimal dynamic price rate policy is not monotonic in wait time. In particular, in addition to the congestion effect often reported in the literature, i.e., the optimal price rate increases in the queue length (measured by the wait time in our setting), we find a compensation effect, meaning that the service provider should lower the price rate when the wait time is longer than a threshold. Compared with the prevalent flat pricing policy, our optimal dynamic pricing policy improves the objective value through admission control, which, in turn, increases the utilization of the server. We use a real data set obtained from a public charging station to calibrate our model with an objective of maximizing the average revenue. We find that our optimal pricing policy outperforms the best flat pricing policy, especially when the arrival rate is low and drivers are impatient. Interestingly, our revenue-maximizing pricing policy also improves social welfare over the flat pricing policy in most of the tested cases.
Queueing Systems, 2013
This paper studies a queuing model where two customer classes compete for a given resource and each customer is dynamically quoted a menu of price and leadtime pairs upon arrival. Customers select their preferred pairs from the menu and the server is obligated to meet the quoted leadtime. Customers have convexconcave delay costs. The firm does not have information on a given customer's type, so the offered menus must be incentive compatible. A menu quotation policy is given and proven to be asymptotically optimal under traditional large-capacity heavy-traffic scaling.
Priority option pricing in an M/M/m queue
Operations Research Letters, 2008
We study a system where the service provider offers priority options. We identify the optimal option pricing policy, by deriving the optimal number a customer would buy and the customer's exercise policy as a function of system congestion, options remaining, time to expiration and possibility of balking.
Priority Assignment Under Imperfect Information on Customer Type Identities
Manufacturing & Service Operations Management, 2009
In many service systems, customers are not served in the order they arrive, but according to a priority scheme that ranks them with respect to their relative "importance." However, it may not be an easy task to determine the importance level of customers, especially when decisions need to be made under limited information. A typical example is from health care: When triage nurses classify patients into different priority groups, they must promptly determine each patients criticality levels with only partial information on their conditions. We consider such a service system where customers are from one of two possible types. The service time and waiting cost for a customer depends on the customer's type. Customers' type identities are not directly available to the service provider; however, each customer provides a signal which is an imperfect indicator of the customer's identity. The service provider uses these signals to determine priority levels for the customers with the objective of minimizing the long-run average waiting cost. In most of the paper, each customer's signal equals the probability that the customer belongs to the type that should have a higher priority and customers incur waiting costs that are linear in time. We first show that increasing the number of priority classes decreases costs and the policy that gives the highest priority to the customer with the highest signal outperforms any finite-class priority policy. We then focus on two-class priority policies and investigate how the optimal policy changes with the system load. We also investigate the properties of "good" signals and find that signals that are larger in convex ordering are more preferable. In a simulation study, we find that when the waiting cost functions are non-decreasing, quadratic, and convex, the policy that assigns the highest priority to the customer with the highest signal performs poorly while the two-class priority policy and an extension of the generalized cµ rule perform well.
We consider a congestible system serving multiple classes of customers who differ in their delay sensitivity and valuation of service (or product). Customers are endowed with convex-concave delay cost functions. A system manager offers a menu of lead times and corresponding prices to arriving customers, who then choose the lead-time-price pair that maximizes their net utility (value minus disutility of delay and price). We investigate how such menus should be chosen dynamically (depending on the system backlog) to maximize welfare. We formulate a novel fluid model of the problem and show that the cost-balancing policy (based on the convex hulls of the delay cost functions) is socially optimal if the system manager can tell customer types apart. If types are indistinguishable to the system manager, the cost-balancing policy is also incentive compatible under social optimization. Finally, we show through a simulation study that the cost-balancing policy does well in the context of the original (stochastic) problem by testing it against various natural benchmarks.
Optimal assignment of dynamic priorities in queuing systems with two types of customers
Automatic Control and Computer Sciences, 2008
We consider queuing systems with two types of customers. For such systems, we develop numerical procedures for computation of optimal dynamic priorities in the case of multiplicative priority functions. The optimality criterion is based on the total queue length for customers of both types. Our technique allows one to take into account waiting-time bounds. The optimization problem is formulated in the language of linear-fractional programming. To illustrate our technique, we present some numerical results at the end of the paper.
The Optimal Admission Threshold in Observable Queues with State Dependent Pricing
Probability in the Engineering and Informational Sciences, 2014
We consider the social welfare model of Naor [20] and revenue-maximization model of Chen and Frank [7], where a single class of delay-sensitive customers seek service from a server with an observable queue, under state dependent pricing. It is known that in this setting both revenue and social welfare can be maximized by a threshold policy, whereby customers are barred from entry once the queue length reaches a certain threshold. However, no explicit expression for this threshold has been found. This paper presents the first derivation of the optimal threshold in closed form, and a surprisingly simple formula for the (maximum) revenue under this optimal threshold. Utilizing properties of the Lambert W function, we also provide explicit scaling results of the optimal threshold as the customer valuation grows. Finally, we present a generalization of our results, allowing for settings with multiple servers.