Departures from queues with changeover times

Magalhães, Marcos Nascimento; Disney, Ralph L.

doi:10.1007/bf01225321

Cited by 4 publications

(3 citation statements)

References 8 publications

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“…The variance of the number of arrivals during one arbitrary service time, written as a function of P 11 , directly follows. For 0 < P 11 < 1, Var(A) = 75 16 + 117 512(1 − P 11 )P 11 .…”

Section: Examplementioning

confidence: 99%

“…A further generalization allowing for Poisson arrivals of groups (batches) of customers of arbitrary random size was investigated by Neuts in [13], obtaining the busy period, queue length and waiting time distributions. The departure process of a related model with single Poisson arrivals and exponential service times was determined by Magalhães and Disney [11]. In that model, the rate of the exponential service times depends on the type of the customer being served as well as that of its predecessor.…”

Section: Introductionmentioning

confidence: 99%

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

Abhishek¹,

Boon²,

Boxma³

et al. 2018

Preprint

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We investigate the transient and stationary queue-length distributions of a class of service systems with correlated service times. The classical M X /G/1 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 J(•) at a service initiation time determines the joint distribution of the subsequent service duration and the state of J(•) 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.

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“…The variance of the number of arrivals during one arbitrary service time, written as a function of P 11 , directly follows. For 0 < P 11 < 1, Var(A) = 75 16 + 117 512(1 − P 11 )P 11 .…”

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Abhishek¹,

Boon²,

Boxma³

et al. 2018

Preprint

View full text Add to dashboard Cite

show abstract

“…The departure process of a related model with single Poisson arrivals and exponential service times was determined by Magalhães and Disney [13]. In that model, the rate of the exponential service times depends on the type of the customer being served as well as that of its predecessor.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2017

View full text Add to dashboard Cite

We investigate the transient and stationary queue length distributions of a class of service systems with correlated service times. The classical M X /G/1 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 J (·) at a service initiation time determines the joint distribution of the subsequent service duration and the state of J (·) 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

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Transient behavior ofM/M ij/1 queues

Daigle

Magalhães

1991

Queueing Syst

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Departures from queues with changeover times

Cited by 4 publications

References 8 publications

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

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

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

Transient behavior ofM/M ij/1 queues

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