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

Woollcott Smith
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Woollcott Smith: University of North Carolina, Chapel Hill, North Carolina

Operations Research, 1972, vol. 20, issue 4, 907-912

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.

Date: 1972
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