THE c - SERVER QUEUE WITH CONSTANT SERVICE TIMES AND A VERSATILE

Classical results of C. D. Crommelin on the c-server queue with constant service times and Poisson input are extended to the case of the versatile Markovian arrival process, introduced by the author. The purely probabilistic analysis of a related problem in Markov chains leads to an algorithm for the evaluation of the stationary distributions of the queue length and waiting time at an arbitrary epoch. As an illustration, the algorithmic steps are discussed in detail for the case where the arrivals form a Narkov-modulated Poisson process.

[1]  M. Neuts.  A Versatile Markovian Point Process , 1979 .

[2]  Shaler Stidham,et al.  The Relation between Customer and Time Averages in Queues , 1980, Oper. Res..

[3]  J. Hunter.  Generalized inverses and their application to applied probability problems , 1982 .

[4]  M. Neuts.  Renewal processes of phase type , 1978 .

[5]  R. Tweedie.  Operator-geometric stationary distributions for markov chains, with application to queueing models , 1982, Advances in Applied Probability.

[7]  M. Neuts.  Some explicit formulas for the steady-state behavior of the queue with semi-Markovian service times , 1977, Advances in Applied Probability.

[8]  S. Brumelle.  On the relation between customer and time averages in queues , 1971 .

[9]  M. Neuts,et al.  Asymptotic behavior of the stationary distributions in the GI/PH/c queue with heterogeneous servers , 1981 .

[10]  Marcel F. Neuts,et al.  The M/G/1 queue with several types of customers and change-over times , 1977, Advances in Applied Probability.

[11]  Marcel F. Neuts,et al.  Some explicit formulas and computational methods for infinite-server queues with phase-type arrivals , 1980, Journal of Applied Probability.

[12]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .

[13]  Marcel F. Neuts.  The Markov Renewal Branching Process , 1974 .

[14]  Marcel F. Neuts,et al.  Matrix-geometric solutions in stochastic models - an algorithmic approach , 1982 .

[15]  V. Ramaswami.  The N/G/1 queue and its detailed analysis , 1980, Advances in Applied Probability.

[16]  John G. Kemeny,et al.  Finite Markov Chains. , 1960 .

[17]  Marcel F. Neuts,et al.  Queues Solvable without Rouché's Theorem , 1979, Oper. Res..