Journal of Applied Probability

Optimal server selection in a queueing loss model with heterogeneous exponential servers, discriminating arrivals, and arbitrary arrival times

Sheldon M. Ross

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Abstract

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.

Article information

Source
J. Appl. Probab., Volume 51, Number 3 (2014), 880-884.

Dates
First available in Project Euclid: 5 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1409932680

Digital Object Identifier
doi:10.1239/jap/1409932680

Mathematical Reviews number (MathSciNet)
MR3256233

Zentralblatt MATH identifier
1306.60145

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22] 90B22: Queues and service [See also 60K25, 68M20]
Secondary: 90B36: Scheduling theory, stochastic [See also 68M20] 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]

Keywords
Loss model server eligibility server selection stochastic maximization

Citation

Ross, Sheldon M. Optimal server selection in a queueing loss model with heterogeneous exponential servers, discriminating arrivals, and arbitrary arrival times. J. Appl. Probab. 51 (2014), no. 3, 880--884. doi:10.1239/jap/1409932680. https://projecteuclid.org/euclid.jap/1409932680


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