Dynamic admission control in a call center with one shared and two dedicated service facilities (original) (raw)
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2005 Asia-Pacific Conference on Communications, 2005
Call admission control and dynamic pricing have been proposed as separate measures to reduce congestion in a network. In this paper, we integrate the call admission control and dynamic pricing problems, formulating them as a Markov Decision Problem (MDP), operating in a multiservice, resourcesharing cellular system. Our model incorporates price-affected behaviour of network users, considering effects on arrivals, retrials and substitutions among services and time. The network exercises admission control, to reject or accept a new connection requests, and price control to set a state-dependent price per bandwidth time with the objective to maximise the long-term revenue. The results show that the proposed method improves revenue and reduces congestion compared to other conventional sub-optimal policies.
Optimal control of admission to a multiserver queue with two arrival streams
IEEE Transactions on Automatic Control, 1992
The problem of nding an optimal admission policy to an M/M/c queue with one controlled and one uncontrolled arrival stream is addressed in this paper. There are two streams of customers (customers of class 1 and 2) that are generated according to independent Poisson processes with constant arrival rates. The service time probability distribution is exponential and does not depend on the class of the customers. Upon arrival a class 1 customer may be admitted or rejected, while incoming class 2 customers are always admitted. A state-dependent reward is earned each time a new class 1 customer enters the system. When the discount factor is small, we show that there exists a stationary admission policy of a threshold type that maximizes the expected total discounted reward over an in nite horizon. A similar result is also obtained when considering the long-run average reward criterion. The proof relies on a new device that consists of a partial construction of the solution of the dynamic programming equation. Applications arising from teletra c analysis are proposed.
Dynamic policies of admission to a two-class system based on customer offers
IIE Transactions, 2002
We consider the problem of dynamic admission control in a Markovian loss queueing system with two classes of jobs with different service rates and random revenues. We establish the existence of an optimal monotone policy. We also show that under certain conditions there exist preferred jobs from either class.
We consider the problem of admission control to an M/M/1 queue under pe- riodic observations with average cost criterion. The admission controller receives the system state information every ¿:th second and can accordingly adjust the acceptance probability for customers who arrive before the next state information update instance. For a period of ¿ seconds, the cost is a linear function of the time average of customer populations and the total number of served customers in that period. The objective is to flnd a stationary deterministic control policy that minimizes the long run average cost. The problem is formulated as a discrete time Markov decision process whose states are fully observable. By taking the control period ¿ to 0 or to 1, the model in question generalizes two classical queueing control problems: the open and the closed loop admission control to an M/M/1 queue. We show that the optimal policy is to admit customers with a non-increasing probability with respect to the...
Optimal control of admission to a station in a closed two queue system
Proceedings of the 1st international conference on Performance evaluation methodolgies and tools - valuetools '06, 2006
We consider a closed queueing system consisting of two stations in tandem. The controller has to make a decision on the number of customers to be admitted for service at the first station so that a long term utility function is maximized. We study the nature of optimal policy for some classes of utility function and transition probability structures. This model can be used to solve many practical closed queueing system problems, like node activation in a rechargeable sensor network. We show that, depending on the number of servers at the various stations, the optimal policy may or may not be greedy.
A dynamic prioritization policy for the callback option in a call center
Flexible Services and Manufacturing Journal, 2021
In this paper, we study the M n ∕M n ∕c∕(K 1 + K 2) + M n system with two finite-size queues where underlying exponential random variables have state-dependent rates. When all servers are busy, upon arrival customers may join the online or the offline/ callback queue or simply balk. Customers waiting in the online queue are impatient and if their patience expires, they may choose to join the callback queue instead of abandoning the system for good. Customers in the callback queue are assumed to be patient. Customers are served following a threshold policy: when the number of customers in the callback queue surpasses a threshold level, the next customer to serve is picked from here. Otherwise, only after a predetermined number of agents are reserved for future arrivals, customers remaining in the callback queue can be served. We conduct an exact analysis of this system and obtain its steady-state performance measures. The times spent in both queues are expressed as Phase-type distributions. With numerical examples, we present how the policy responds when shorter callback times are promised or customer characteristics vary. Keywords The M n ∕M n ∕c∕(K 1 + K 2) + M n queue • Impatient customers • Callback option • Phase-type distribution • Call centers * Barış Balcıoglu
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.
Optimality of Trunk Reservation for an M/M/K/N Queue with Several Customer Types and Holding Costs
Probability in the Engineering and Informational Sciences, 2011
In this article we study optimal admission to an M/M/k/N queue with several customer types. The reward structure consists of revenues collected from admitted customers and holding costs, both of which depend on customer types. This article studies average rewards per unit time and describes the structures of stationary optimal, canonical, bias optimal, and Blackwell optimal policies. Similar to the case without holding costs, bias optimal and Blackwell optimal policies are unique, coincide, and have a trunk reservation form with the largest optimal control level for each customer type. Problems with one holding cost rate have been studied previously in the literature.
Managing service facilities with endogenous arrival and service rates
International Transactions in Operational Research, 2017
We conduct a simulation-based experiment to analyze how past experiences in a service facility system affect customers' and service providers' behavior. We study the problem faced by service providers in deciding by how much to adjust the capacity of their facility when captive repeat customers choose which facility to join based on their expected sojourn times. The customers' decision-making process differs from that of service providers in that the former is based on the customers' experience, whereas the latter is based on the most recent information service providers have regarding demand. Customers use their previous experience and that of their neighbors to update their perceptions of the future average sojourn time, whereas service providers form perceptions of the future arrival rate. We use cellular automata to model the interaction between customers and service providers. We perform simulations to assess the way the customers' and service providers' decisions evolve and affect system behavior. Our findings demonstrate that the system we study possesses a certain degree of path dependence. The primary conclusion is that the more conservative service providers are regarding new information, the larger the market share they achieve, and the lower the probability that their facility will shut down.