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The slow server problem: a queue with stalling

  • Michael Rubinovitch (a1)

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.

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Copyright

Corresponding author

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

Footnotes

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

Footnotes

References

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Bailey, N. T. J. (1957) Some further results in the non-equilibrium theory of a simple queue. J. R. Statist. Soc. B19, 326333.
Bell, C. E. and Stidham, S. (1983) Individual versus social optimization in the allocation of customers to alternative servers. Management Sci. 29, 831839.
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.
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.
Naor, P. (1969) On regulation of queue size by levying tolls. Econometrica 37, 1524.
Prabhu, N. U. (1965a) Stochastic Processes. Macmillan, New York.
Prabhu, N. U. (1965b) Queues and Inventories. Wiley, New York.
Rubinovitch, M. (1985) The slow server problem. J. Appl. Prob. 22, 205213.
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.

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The slow server problem: a queue with stalling

  • Michael Rubinovitch (a1)

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