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The slow server problem: a queue with stalling

Published online by Cambridge University Press:  14 July 2016

Michael Rubinovitch*
Affiliation:
Technion — Israel Institute of Technology
*
Postal address: Faculty of Industrial Engineering and Management, Technion — Israel Institute of Technology, Haifa 32000, Israel.

Abstract

A queue with Poisson arrivals and two different exponential servers is considered. It is assumed that customers are allowed to stall, i.e., to wait for a busy fast server at times when the slow server is free. A stochastic analysis of the queue is given, steady-state probabilities are computed, and policies for overall optimization are characterized and computed. The issue of individual customer's optimization versus overall optimization is also discussed.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1985 

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Footnotes

Research carried out while the author was on leave at Northwestern University.

References

Bailey, N. T. J. (1957) Some further results in the non-equilibrium theory of a simple queue. J. R. Statist. Soc. B19, 326333.Google Scholar
Bell, C. E. and Stidham, S. (1983) Individual versus social optimization in the allocation of customers to alternative servers. Management Sci. 29, 831839.Google Scholar
Larsen, R. L. (1981) Control of multiple exponential servers with applications to computer systems. Computer Science Technical Report Series No. TR-1041, University of Maryland, College Park.Google Scholar
Lin, W. and Kumar, P. R. (1982) Optimal control of a queueing system with two heterogeneous servers. Mathematics Research Report No. 82-83, Department of Mathematics, University of Maryland, Baltimore County.Google Scholar
Naor, P. (1969) On regulation of queue size by levying tolls. Econometrica 37, 1524.Google Scholar
Prabhu, N. U. (1965a) Stochastic Processes. Macmillan, New York.Google Scholar
Prabhu, N. U. (1965b) Queues and Inventories. Wiley, New York.Google Scholar
Rubinovitch, M. (1985) The slow server problem. J. Appl. Prob. 22, 205213.Google Scholar
Walrand, J. (1983) A note on ‘Optimal control of a queueing system with two heterogeneous servers.’ Technical Report, Department of Electrical Engineering and Computer Sciences and Electronic Research Laboratory, University of California, Berkeley.Google Scholar