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The general N server finite queue
- Source :
- Journal of Applied Probability. 8:828-834
- Publication Year :
- 1971
- Publisher :
- Cambridge University Press (CUP), 1971.
-
Abstract
- Kingman (1962) studied the effect of queue discipline on the mean and variance of the waiting time. He made no assumptions regarding the stochastic nature of the input and the service distributions, except that the input and service processes are independent of each other. When the following two conditions hold: (a) no server sits idle while there are customers waiting to be served; (b) the busy period is finite with probability one (i.e., the queue empties infinitely often with probability one); he has shown that the mean waiting time is independent of the queue discipline and the variance of the waiting time is a minimum when the customers are served in order of their arrival. Conditions (a) and (b) will henceforward be called Kingman conditions and a queueing system satisfying Kingman conditions will be referred to in the text as a Kingman queue.
- Subjects :
- Statistics and Probability
D/M/1 queue
Discrete mathematics
M/G/k queue
General Mathematics
010102 general mathematics
M/D/1 queue
M/M/1 queue
M/D/c queue
G/G/1 queue
01 natural sciences
010104 statistics & probability
M/G/1 queue
M/M/c queue
0101 mathematics
Statistics, Probability and Uncertainty
Mathematics
Subjects
Details
- ISSN :
- 14756072 and 00219002
- Volume :
- 8
- Database :
- OpenAIRE
- Journal :
- Journal of Applied Probability
- Accession number :
- edsair.doi...........06e4bc4eb2bec4fd0f9d99714a84f245