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Technical Note—The Infinitely-Many-Server Queue with Semi-Markovian Arrivals and Customer-Dependent Exponential Service Times

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  • Woollcott Smith

    (University of North Carolina, Chapel Hill, North Carolina)

Abstract

This note studies an infinitely-many-server queue with N types of customers arriving according to a semi-Markov process. The service times are independent exponential random variables with means 1/μ i , where i is the type of customer being served. The stationary distribution of the embedded Markov chain and the limiting distribution of the continuous-time process are obtained.

Suggested Citation

  • Woollcott Smith, 1972. "Technical Note—The Infinitely-Many-Server Queue with Semi-Markovian Arrivals and Customer-Dependent Exponential Service Times," Operations Research, INFORMS, vol. 20(4), pages 907-912, August.
    • Handle: RePEc:inm:oropre:v:20:y:1972:i:4:p:907-912
    DOI: 10.1287/opre.20.4.907
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    Cited by:

    1. Anatoly Nazarov & Alexander Dudin & Alexander Moiseev, 2022. "Pseudo Steady-State Period in Non-Stationary Infinite-Server Queue with State Dependent Arrival Intensity," Mathematics, MDPI, vol. 10(15), pages 1-12, July.
    2. Landy Rabehasaina & Jae-Kyung Woo, 2018. "On a multivariate renewal-reward process involving time delays and discounting: applications to IBNR processes and infinite server queues," Queueing Systems: Theory and Applications, Springer, vol. 90(3), pages 307-350, December.

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