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Throughput maximization in a loss queueing system with heterogeneous servers

Published online by Cambridge University Press:  14 July 2016

Matthew J. Sobel
Matthew J. Sobel*
Affiliation:
SUNY at Stony Brook
*
∗Postal address: W. A. Harriman School of Management and Policy, SUNY at Stony Brook, Stony Brook, NY 1 1794-3775, USA.
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Abstract

Assigning each arriving customer to the fastest idle server is shown to maximize throughput (equivalently, minimize blocking probability) in a queueing model with Poisson arrivals, heterogeneous exponential servers, and no waiting room. If a cost structure is imposed on this model, under specified conditions the same policy minimizes the expected discounted cost and the long-run average cost per unit time.

Keywords

M/M/c/c QUEUEHETEROGENEOUS SERVERSTHROUGHPUT MAXIMIZATIONMATCHING CUSTOMERS WITH SERVERS
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 3 , September 1990 , pp. 693 - 700
Copyright
Copyright © Applied Probability Trust 1990 

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References

Beltrami, E. (1977) Models for Public Systems Analysis. Academic Press, New York.Google Scholar
Carpenito, T. A. and White, J. A. (1974) The allocation of non-identical machines among non-identical servers. Rept. No. 7405, Dept, of Ind. Eng. & Oper. Res., Va. Polytechnic Inst. & State Univ.Google Scholar
Derman, C, Lieberman, G. L. and Ross, S. M. (1978) A renewal decision problem. Management Sci. 24, 554–561.Google Scholar
Derman, C., Lieberman, G. L. and Ross, S. M. (1980) On the optimal assignment of servers and a repairman. J. Appl. Prob. 17, 577–581.Google Scholar
Derman, C. and Smith, D. R. (1979) Renewal decision problem-random horizon. Math. Operat. Res. 4, 225–232.Google Scholar
Green, L. (1984) Multiple dispatch queueing model of police patrol operations. Management Sci. 30, 653–664.CrossRefGoogle Scholar
Heyman, D. P. and Sobel, M. J. (1984) Stochastic Models in Operations Research, Volume II: Stochastic Optimization. McGraw-Hill, New York.Google Scholar
Jarvis, J. J. (1981) Optimal assignments in a Markovian queueing system. Comp. Operat. Res. 8, 17–23.CrossRefGoogle Scholar
Katehakis, M. N. (1985) A note on the hypercube model. Operat. Res. Let. 3, 319–322.CrossRefGoogle Scholar
Katehakis, M. N. and Derman, C. (1984) Optimal repair allocation in a series system. Math. Operat. Res. 9, 615–623.Google Scholar
Katehakis, M. N. and Johri, P. K. (1984) Optimal repair of a 2-component series system with partially repairable components. IEEE Trans. Reliability 33, 427–430.Google Scholar
Katehakis, M. N. and Levine, A. (1986) Allocation of distinguishable servers. Comp. Operat. Res. 13, 85–93.Google Scholar
Larson, R. C. (1974) A hypercube queueing model for facility location and redistricting in urban emergency services. Comp. Operat. Res. 1, 67–95.Google Scholar
Larson, R. C. and Odoni, A. R. (1981) Urban Operations Research. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
Serfozo, R. (1979) An equivalence between continuous and discrete time Markov decision processes. Operat. Res. 27, 616–620.CrossRefGoogle Scholar
Serfozo, R. (1985) Allocation of servers for stochastic service stations with one overflow station. Management Sci. 31, 1011–1018.Google Scholar
Seth, K. (1977) Optimal service policies, just after idle periods, in two-server heterogeneous queuing systems. Operat. Res. 25, 356–360.Google Scholar
Smith, D. R. (1978a) Optimal repair of a series system. Operat. Res. 26, 653–662.Google Scholar
Smith, D. R. (1978b) Optimal repairmen allocation-asymptotic results. Management Sci. 24, 665–674.Google Scholar
Sobel, M. J. (1982) The optimality of full service policies. Operat. Res. 30, 636–649.CrossRefGoogle Scholar
Weber, R. R. (1978) On the optimal assignment of customers to parallel servers. J. Appl. Prob. 15, 406–413.CrossRefGoogle Scholar
Wolff, R. W. (1982) Poisson arrivals see time averages. Operat. Res. 30, 223–231.Google Scholar
Winston, W. (1977) Optimality of the shortest line discipline. J. Appl. Prob. 14, 181–189.Google Scholar