Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-25T04:13:23.792Z Has data issue: false hasContentIssue false
  • English
  • Français

The impact of the composition of the customer base in general queueing models

Published online by Cambridge University Press:  14 July 2016

A. Federgruen  and
H. Groenevelt
A. Federgruen*
Affiliation:
Columbia University
H. Groenevelt*
Affiliation:
University of Rochester
*
∗Postal address: Graduate School of Business, Uris Hall, Columbia University, New York, NY 10027, USA.
∗∗Postal address: William E. Simon Graduate School of Business Administration, University of Rochester, Rochester, NY, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider general queueing models dealing with multiple classes of customers and address the question under what conditions and in what (stochastic) sense the marginal increase in various performance measures, resulting from the addition of a new class of customers to an existing system, is larger than if the same class were added to a system dealing with only a subset of its current customer base.

Our results enhance our understanding of the dependence of various performance measures with respect to the composition of the customer base. In addition they translate readily into convexity results in an (appropriately defined) arrival rate.

Keywords

MULTIPLE CUSTOMER CLASSESSTRUCTURED PROPERTIES OF PERFORMANCECONVEXITY IN ARRIVAL RATE
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 3 , September 1987 , pp. 709 - 724
Copyright
Copyright © Applied Probability Trust 1987 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Edmonds, J. (1970) Submodular functions, matroids and certain polyhedra, in Combinatorial Structures and Their Applications , ed. Guy, R. et al., Gordon and Breach, New York, 69–87.Google Scholar
Federgruen, A. Groenevelt, H. (1986a) The greedy procedure for resource allocation problems: Necessary and sufficient conditions for optimality. Operat. Res. Google Scholar
Federgruen, A. Groenevelt, H. (1986b) Characterization and optimization of achievable performance in queueing systems. Operat. Res. To appear.Google Scholar
Federgruen, A Groenevelt, H. (1986c) M/G/c queueing systems with multiple customer classes: characterization and control of achievable performance under nonpreemptive priority rules. Working Paper, Graduate School of Business, Columbia University, New York.Google Scholar
Gelenbe, E. Mitrani, I. (1980) Analysis and Synthesis of Computer Systems. Academic Press, New York.Google Scholar
Grassmann, W. (1983) The convexity of the mean queue size of the M/M/c queue with respect to the traffic intensity. J. Appl. Prob. 20, 916–919.Google Scholar
Groenevelt, H. (1985) Two algorithms for maximizing a separable concave function over a polymatroid feasible region. Graduate School of Management Working Paper, University of Rochester, Rochester, N.Y. Google Scholar
Harel, A. Zipkin, P. (1984) Strong convexity results for queueing systems with applications in production and telecommunications. Operat. Res. To appear.Google Scholar
Harel, A. Zipkin, P. (1987) The convexity of a general performance measure for multiserver queues J. Appl. Prob. 24, 725–736.Google Scholar
Heyman, D. Sobel, M. (1982) Stochastic Models in Operations Research , Vol. I, McGraw-Hill, New York.Google Scholar
Kamae, T. Krengel, U. 'Brien, G. (1977) Stochastic inequalities on partially ordered spaces. Ann. Prob. 5, 899–912 Google Scholar
Lee, H. Cohen, M. (1983) A note on the convexity of performance measures of M/M/c queueing systems. J. Appl. Prob. 20, 920–923.Google Scholar
Lindvall, T. (1979) A note on coupling of birth and death processes. J. Appl. Prob. 16, 505–512.Google Scholar
Marshall, K. Wolff, R. (1971) Customer average and time average queue lengths and waiting times. J. Appl. Prob. 8, 535–542.Google Scholar
Nemhauser, G. Wolsey, L. Fisher, M. (1978) An analysis of algorithms for maximizing submodular set functions. Math. Progr. 14, 265–294.Google Scholar
Ross, S. (1978) Average delay in queues with nonstationary Poisson arrivals. J. Appl. Prob. 15, 602–609.Google Scholar
Smith, D. Whitt, W. (1981) Resource sharing for efficiency in traffic systems. Bell Syst. Tech. J. 60, 39–55.Google Scholar
Sonderman, D. (1980) Comparing semi-Markov processes. Math. Operat. Res. 5, 110–120.Google Scholar
Svoronos, T. Green, L. (1985) On the validity of Ross's conjecture for finite capacity queueing systems with nonstationary arrivals and exponential service times. Working Paper No. 85–22, Graduate School of Business, Columbia University, New York.Google Scholar
Tu, H. Kumin, H. (1983) A convexity result for a class of GI/G/1 queueing systems. Operat. Res. 31, 948–950.Google Scholar
Weber, R. (1980) On the marginal benefit of adding servers to G/GI/m queues. Management Sci. 26, 946–951.Google Scholar
Weber, R. (1983) A note on waiting times in single server queues. Operat. Res. 31, 950–951. Welsh, D. (1976) Matroid Theory. Academic Press, London.Google Scholar
Whitt, W. (1981) Comparing counting processes and queues. Adv. Appl. Prob. 13, 207–220.Google Scholar
Wolff, R. (1977) An upper bound for multi-channel queues. J. Appl. Prob. 14, 884–888.Google Scholar