A Single Queue with Mutually Replacing m Servers

Kailash C. Madan


Customers arriving in a Poisson stream are served one by one exponentially by one of the m servers S 1, S 2, S 3, . . . , S m. A
server who has just completed a service either continues the next service or is replaced by another server. The replacement
of a server at each service completion is governed by a probabilistic criterion of availability of servers. Transient solutions
in terms of Laplace transforms of the probability generating functions are obtained and among some special cases the
earlier known results for the case of 2 servers are deduced. The steady state solutions and the average queue sizes have
been obtained for some particular cases.

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DOI: http://dx.doi.org/10.5539/jmr.v3n1p3

Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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