A single-server queue with batch arrivals and semi-Markov services

Abhishek, M.A.A. Boon, O.J. Boxma, R. Núñez-Queija

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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Uittreksel

We investigate the transient and stationary queue length distributions of a class of service systems with correlated service times. The classical (Formula presented.) queue with semi-Markov service times is the most prominent example in this class and serves as a vehicle to display our results. The sequence of service times is governed by a modulating process J(t). The state of (Formula presented.) at a service initiation time determines the joint distribution of the subsequent service duration and the state of (Formula presented.) at the next service initiation. Several earlier works have imposed technical conditions, on the zeros of a matrix determinant arising in the analysis, that are required in the computation of the stationary queue length probabilities. The imposed conditions in several of these articles are difficult or impossible to verify. Without such assumptions, we determine both the transient and the steady-state joint distribution of the number of customers immediately after a departure and the state of the process J(t) at the start of the next service. We numerically investigate how the mean queue length is affected by variability in the number of customers that arrive during a single service time. Our main observations here are that increasing variability may reduce the mean queue length, and that the Markovian dependence of service times can lead to large queue lengths, even if the system is not in heavy traffic.

Originele taal-2Engels
Pagina's (van-tot)217-240
Aantal pagina's24
TijdschriftQueueing Systems
Volume86
Nummer van het tijdschrift3-4
DOI's
StatusGepubliceerd - 27 mei 2017

Vingerafdruk

Batch Arrivals
Single Server Queue
Servers
Queue Length
Joint Distribution
Customers
Queue
Batch
Queue Length Distribution
Heavy Traffic
Steady-state Distribution
Stationary Distribution
Immediately
Determinant
Verify

Citeer dit

Abhishek, ; Boon, M.A.A. ; Boxma, O.J. ; Núñez-Queija, R. / A single-server queue with batch arrivals and semi-Markov services. In: Queueing Systems. 2017 ; Vol. 86, Nr. 3-4. blz. 217-240.
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A single-server queue with batch arrivals and semi-Markov services. / Abhishek, ; Boon, M.A.A.; Boxma, O.J.; Núñez-Queija, R.

In: Queueing Systems, Vol. 86, Nr. 3-4, 27.05.2017, blz. 217-240.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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