Improving Service by Informing Customers About Anticipated Delays

Management Science - Tập 45 Số 2 - Trang 192-207 - 1999
Ward Whitt1
1AT&T Labs, Shannon Laboratory, 180 Park Avenue, Florham Park, New Jersey 07932-0971

Tóm tắt

This paper investigates the effect upon performance in a service system, such as a telephone call center, of giving waiting customers state information. In particular, the paper studies two M/M/s/r queueing models with balking and reneging. For simplicity, it is assumed that each customer is willing to wait a fixed time before beginning service. However, customers differ, so the delay tolerances for successive customers are random. In particular, it is assumed that the delay tolerance of each customer is zero with probability β, and is exponentially distributed with mean α−1 conditional on the delay tolerance being positive. Let N be the number of customers found by an arrival. In Model 1, no state information is provided, so that if N ≥ s, the customer balks with probability β; if the customer enters the system, he reneges after an exponentially distributed time with mean α−1 if he has not begun service by that time. In Model 2, if N = s + k ≥ s, then the customer is told the system state k and the remaining service times of all customers in the system, so that he balks with probability β + (1 − β)(1 − qk), where qk = P(T > Sk), T is exponentially distributed with mean α−1, Sk is the sum of k + 1 independent exponential random variables each with mean (sμ)−1, and μ−1 is the mean service time. In Model 2, all reneging is replaced by balking. The number of customers in the system for Model 1 is shown to be larger than that for Model 2 in the likelihood-ratio stochastic ordering. Thus, customers are more likely to be blocked in Model 1 and are more likely to be served without waiting in Model 2. Algorithms are also developed for computing important performance measures in these, and more general, birth-and-death models.

Từ khóa


Tài liệu tham khảo

10.1287/ijoc.7.1.36

Barlow R. E., 1972, Statistical Inference Under Order Restrictions

Basawa I. V., 1980, Statistical Inference for Stochastic Processes

Boxma O. J., 1995, Proc. ITC 14, 743

10.1109/90.469948

Courtois P. J., 1977, Decomposability

10.1287/mnsc.41.6.1107

10.1109/TCOM.1981.1094971

10.1007/BF01158472

Feller W., 1971, An Introduction to Probability Theory and its Applications, 2

10.1287/mnsc.37.1.84

Gross D., 1985, Fundamentals of Queueing Theory, 2

Hall R. W., 1991, Queueing Methods for Services and Manufacturing

Heyman D. P., 1982, Stochastic Models in Operations Research

10.2307/1251932

Katz K. L., 1991, Sloane Management Rev., 32, 44

10.1214/aoap/1177005872

10.1287/opre.44.6.976

Rappaport D. M., 1996, Bus. Comm. Rev., 44

10.1007/978-1-4471-2126-8

Shaked M., 1994, Stochastic Orders and Their Applications

10.1002/j.1538-7305.1981.tb00221.x

10.2307/1252269

10.2307/1426475

10.1002/j.1538-7305.1985.tb00038.x

10.1287/mnsc.37.3.307

10.1111/j.1937-5956.1993.tb00094.x

10.1287/mnsc.45.6.870

Wolff R. W., 1989, Stochastic Modelling and the Theory of Queues

Thông tin
Thông tin xuất bản

Management Science

Tập 45 Số 2

192-207

Thông tin tác giả