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The delay distribution of a type k customer in a first-come-first-served MMAP[K]/PH[K]/1 queue
- Source :
- Journal of applied probability
- Publication Year :
- 2002
- Publisher :
- Cambridge University Press (CUP), 2002.
-
Abstract
- This paper presents an algorithmic procedure to calculate the delay distribution of a type k customer in a first-come-first-served (FCFS) discrete-time queueing system with multiple types of customers, where each type has different service requirements (the MMAP[K]/PH[K]/1 queue). First, we develop a procedure, using matrix analytical methods, to handle arrival processes that do not allow batch arrivals to occur. Next, we show that this technique can be generalized to arrival processes that do allow batch arrivals to occur. We end the paper by presenting some numerical examples.
- Subjects :
- Discrete mathematics
Statistics and Probability
Queueing theory
mmap
M/G/k queue
General Mathematics
010102 general mathematics
01 natural sciences
010104 statistics & probability
First-come, first-served
Probability distribution
Phase-type distribution
Markovian arrival process
0101 mathematics
Statistics, Probability and Uncertainty
Queue
Algorithm
Mathematics
Subjects
Details
- ISSN :
- 14756072 and 00219002
- Volume :
- 39
- Database :
- OpenAIRE
- Journal :
- Journal of Applied Probability
- Accession number :
- edsair.doi.dedup.....29a028371a6bd75291e475a489f11aec