Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-25T05:47:05.065Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal Server Selection in a Queueing Loss Model with Heterogeneous Exponential Servers, Discriminating Arrivals, and Arbitrary Arrival Times

Part of: Computer system organization Special processes Operations research and management science

Published online by Cambridge University Press:  30 January 2018

Sheldon M. Ross
Sheldon M. Ross*
Affiliation:
University of Southern California
*
∗ Postal address: Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089, USA. Email address: smross@usc.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider a multiple server queueing loss system where the service times of server i are exponential with rate μi, where μi decreases in i. Arrivals have associated vectors (X1, …, Xn) of binary variables, with Xi = 1 indicating that server i is eligible to serve that arrival. Arrivals finding no idle eligible servers are lost. Letting Ij be the indicator variable for the event that the jth arrival enters service, we show that, for any arrival process, the policy that assigns arrivals to the smallest numbered idle eligible server stochastically maximizes the vector (I1, …, Ir) for every r if the eligibility vector of arrivals is either (a) exchangeable, or (b) a vector of independent variables for which P(Xi = 1) increases in i.

Keywords

Loss modelserver eligibilityserver selectionstochastic maximization

MSC classification

Primary: 60K25: Queueing theory 90B22: Queues and service
Secondary: 90B36: Scheduling theory, stochastic 68M20: Performance evaluation; queueing; scheduling
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 3 , September 2014 , pp. 880 - 884
Copyright
© Applied Probability Trust 

Footnotes

This material is based upon work supported by the National Science Foundation under contract/grant number CMMI1233337.

References

Cooper, R. B. (1976). Queues with ordered servers that work at different rates. Opsearch 13, 69–78.Google Scholar
Derman, C., Lieberman, G. J. and Ross, S. M. (1980). On the optimal assignment of servers and a repairman. J. Appl. Prob. 17, 577–581.Google Scholar
Gregory, G. and Litton, C. D. (1975). A conveyer model with exponential service times. Internat. J. Production Res. 13, 1–7.Google Scholar
Hordijk, A. and Koole, G. (1992). On the assignment of customers to parallel queues. Prob. Eng. Inf. Sci. 6, 495–511.CrossRefGoogle Scholar
Katehakis, M. N. (1985). A note on the hypercube model. Operat. Res. Lett. 3, 319–322.Google Scholar
Matsui, M. and Fukuta, J. (1977). On a multichannel queueing system with ordered entry and heterogeneous servers. AIIE Trans. 9, 209–214.Google Scholar
Sobel, M. J. (1990). Throughput maximization in a loss queueing system with heterogeneous servers. J. Appl. Prob. 27, 693–700.Google Scholar
Yao, D. D. (1987). The arrangement of servers in an ordered-entry system. Operat. Res. 35, 759–763.Google Scholar