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THE IMPACTS OF CUSTOMERS’ DELAY-RISK SENSITIVITIES ON A QUEUE WITH BALKING

Published online by Cambridge University Press:  30 April 2009

Pengfei Guo  and
Paul Zipkin
Pengfei Guo
Affiliation:
Department of Logistics and Maritime Studies, Hong Kong Polytechnic University, Hung Hom, Hong Kong Email: lgtpguo@polyu.edu.hk
Paul Zipkin
Affiliation:
The Fuqua School of Business, Duke University, Durham, NC 27708, USA Email: paul.zipkin@duke.edu
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Abstract

Congestion and its uncertainty are big factors affecting customers’ decision to join a queue or balk. In a queueing system, congestion itself is resulted from the aggregate joining behavior of other customers. Therefore, the property of the whole group of arriving customers affects the equilibrium behavior of the queue. In this paper, we assume each individual customer has a utility function which includes a basic cost function, common to all customers, and a customer-specific weight measuring sensitivity to delay. We investigate the impacts on the average customer utility and the throughput of the queueing system of different cost functions and weight distributions. Specifically, we compare systems where these parameters are related by various stochastic orders, under different information scenarios. We also explore the relationship between customer characteristics and the value of information.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 23 , Issue 3 , July 2009 , pp. 409 - 432
Copyright
Copyright © Cambridge University Press 2009

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References

1.Armony, M. & Maglaras, C. (2004). On customer contact centers with a call-back option: Customer decisions, routing rules, and system design. Operations Research 52: 271–292.CrossRefGoogle Scholar
2.Armony, M. & Maglaras, C. (2004). Contact center with a call-back option and real-time delay information. Operations Research 52: 527–545.CrossRefGoogle Scholar
3.Armony, M., Shimkin, N. & Whitt, W. (2005). The impacts of delay announcements in many-server queues with abandonment. Working paper, New York University.Google Scholar
4.Dai, L. & Chao, X. (1996). Comparing single-server loss systems in random environment. IEEE Transaction on Automatic Control 41: 1079–1083.Google Scholar
5.de Palma, A., Lindsey, R. & Picard, N. (2007). Congestion, risk aversion and the value of information. Working paper. University of Alberta, Canada.Google Scholar
6.Chao, X. & Dai, L. (1995). A monotonicity result for a single-server loss system. Journal of Applied Probability 32: 1112–1117.CrossRefGoogle Scholar
7.Edelson, M. & Hildebrand, K. (1975). Congestion tolls for Poisson queueing processes. Econometrica 43: 81–92.CrossRefGoogle Scholar
8.Freixas, X. & Kihlstrom, R. (1984). Risk aversion and information demand. In Boyer, M. and Kihlstrom, R., eds., Bayesian Models in Economic Theory. Amsterdam: North Holland.Google Scholar
9.Gavish, B. & Schweitzer, P. (1973). Queue regulation policies using full information. Working paper, Israel Scientific Center.Google Scholar
10.Guo, P. & Zipkin, P. (2007). Analysis and comparison of queues with different levels of delay information. Management Science 53: 962–970.CrossRefGoogle Scholar
11.Guo, P. & Zipkin, P. (2006). The effects of information on a queue with balking and phase-type service times. Forthcoming inNaval Research Logistics.Google Scholar
12.Hassin, R. (2007). Information and uncertainty in a queueing system. Probability in the Engineering and Informational Sciences 21: 361–380.CrossRefGoogle Scholar
13.Hassin, R. & Haviv, M. (2003). To Queue or Not to Queue: Equilibrium Behavior in Queuing Systems. Boston/Dordrecht/London: Kluwer Academic Publishers.CrossRefGoogle Scholar
14.Heyman, D. (1982). On Ross's conjectures about queues with non-stationary Poisson arrivals. Journal of Applied Probability 19: 245–249.CrossRefGoogle Scholar
15.Hilton, R. (1981). The determinants of information value: Synthesizing some general results. Management Science 27: 57–64.CrossRefGoogle Scholar
16.Karlin, S. (1968). Total Positivity Vol. 1. Stanford, California: Stanford University Press.Google Scholar
17.Müller, A. & Stoyan, D. (2002). Comparison Methods for Stochastic Models and Risks. John Wiley & Sons.Google Scholar
18.Nadiminti, R., Mukhopadhyay, T. & Kriebel, C. (1996). Risk version and the value of information. Decision Support Systems 16: 241–254.CrossRefGoogle Scholar
19.Naor, P. (1969). The regulation of queue size by levying tolls. Econometrica 37: 15–24.CrossRefGoogle Scholar
20.Pratt, J. (1964). Risk aversion in the small and in the large. Econometrica 32: 122–136.CrossRefGoogle Scholar
21.Rolski, T. (1990). Queues with nonstationary inputs. Queueing Systems 5: 113–130.CrossRefGoogle Scholar
22.Ross, S. (1978). Average delay in queues with nonstationary arrivals. Journal of Applied Probability 15: 602–609.CrossRefGoogle Scholar
23.Schroeter, R. (1982). The costs of concealing the customer queue. Working paper. Department of Economics. Iowa State University.Google Scholar
24.Shaked, M. & Shanthikumar, J. (1994). Stochastic Orders and Their Applications. Boston, San Diego, New York, London, Sydney, Tokyo, Toronto: Academic Press.Google Scholar
25.Shimkin, N. & Mandelbaum, A. (2004). Rational abandonment from tele-queues: nonlinear waiting cost with heterogeneous preferences, Queueing Systems 47: 117–146.CrossRefGoogle Scholar
26.Stidham, S. (1985). Optimal control of admission to a queuing system. IEEE Transaction on Automatic Control 30: 705–13.CrossRefGoogle Scholar
27.Whitt, W. (1999). Improving service by informing customers about anticipated delay. Management Science 45: 192–207.CrossRefGoogle Scholar
28.Whitt, W. (2006). Sensitivity of performance in the Erlang-A queueing model to changes in the model parameters. Operations Research 54: 247–260.CrossRefGoogle Scholar
29.Willinger, M. (1989). Risk aversion and the value of information. Journal of Risk and Insurance 56: 320–328.CrossRefGoogle Scholar