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Some explicit formulas and computational methods for infinite-server queues with phase-type arrivals
- Source :
- Journal of Applied Probability. 17:498-514
- Publication Year :
- 1980
- Publisher :
- Cambridge University Press (CUP), 1980.
-
Abstract
- This paper discusses infinite server queues whose input is a Phase Type Renewal Process. The problems of obtaining the transient and steady-state distributions and moments of the queue length are reduced to the solution of certain well-behaved systems of linear differential equations. Sample computations are provided with as many as ten phases. The paper contains some useful explicit formulas and also discusses the interesting special case where the service time is also of phase type. The Phase Type Distributions include a wide variety of models such as generalized Erlang, hyperexponential (mixtures of a finite number of exponentials) as very special cases and possess great versatality in modeling a number of interesting qualitative features such as bimodality.
- Subjects :
- Discrete mathematics
Statistics and Probability
Queueing theory
Differential equation
General Mathematics
010102 general mathematics
Erlang (unit)
01 natural sciences
Computer Science::Performance
010104 statistics & probability
Linear differential equation
Applied mathematics
Renewal theory
Special case
0101 mathematics
Statistics, Probability and Uncertainty
Finite set
Queue
Mathematics
Subjects
Details
- ISSN :
- 14756072 and 00219002
- Volume :
- 17
- Database :
- OpenAIRE
- Journal :
- Journal of Applied Probability
- Accession number :
- edsair.doi.dedup.....06471efbf5fe64256036c5c7e28a99bd