scholarly journals Single-Server Queue with Markov-Dependent Inter-Arrival and Service Times

2006 ◽  
Vol 54 (1) ◽  
pp. 79-79
Author(s):  
I. J. B. F. Adan ◽  
V. G. Kulkarni
Keyword(s):  
Single Server ◽  
Single Server Queue ◽  
Server Queue ◽  
Service Times

The single-server queue with service depending on queue size and with the preemptive-resume last-come–first-served queue discipline

1987 ◽  
Vol 24 (03) ◽  
pp. 758-767
Author(s):  
D. Fakinos
Keyword(s):  
Queueing System ◽  
Limiting Distribution ◽  
Single Server ◽  
Queue Size ◽  
Single Server Queue ◽  
Preemptive Resume ◽  
Server Queue ◽  
Queue Discipline ◽  
Service Times

This paper studies theGI/G/1 queueing system assuming that customers have service times depending on the queue size and also that they are served in accordance with the preemptive-resume last-come–first-served queue discipline. Expressions are given for the limiting distribution of the queue size and the remaining durations of the corresponding services, when the system is considered at arrival epochs, at departure epochs and continuously in time. Also these results are applied to some particular cases of the above queueing system.

Logarithmic asymptotics for steady-state tail probabilities in a single-server queue

1994 ◽  
Vol 31 (A) ◽  
pp. 131-156 ◽  
Author(s):  
Peter W. Glynn ◽  
Ward Whitt
Keyword(s):  
Steady State ◽  
Decay Rate ◽  
Partial Sums ◽  
Asymptotic Result ◽  
Service Discipline ◽  
Single Server ◽  
Single Server Queue ◽  
Asymptotic Decay ◽  
Server Queue ◽  
Service Times

We consider the standard single-server queue with unlimited waiting space and the first-in first-out service discipline, but without any explicit independence conditions on the interarrival and service times. We find conditions for the steady-state waiting-time distribution to have asymptotics of the form x–1 log P(W> x) → –θ ∗as x → ∞for θ ∗ > 0. We require only stationarity of the basic sequence of service times minus interarrival times and a Gärtner–Ellis condition for the cumulant generating function of the associated partial sums, i.e. n–1 log E exp (θSn) → ψ (θ) as n → ∞, plus regularity conditions on the decay rate function ψ. The asymptotic decay rate θ is the root of the equation ψ (θ) = 0. This result in turn implies a corresponding asymptotic result for the steady-state workload in a queue with general non-decreasing input. This asymptotic result covers the case of multiple independent sources, so that it provides additional theoretical support for a concept of effective bandwidths for admission control in multiclass queues based on asymptotic decay rates.

Finite-pool queueing with heavy-tailed services

2017 ◽  
Vol 54 (3) ◽  
pp. 921-942
Author(s):  
Gianmarco Bet ◽  
Remco van der Hofstad ◽  
Johan S. H. van Leeuwaarden
Keyword(s):  
Head Start ◽  
Stable Process ◽  
Scaling Limit ◽  
Asymptotic Result ◽  
Single Server ◽  
Single Server Queue ◽  
Long Period ◽  
Server Queue ◽  
Service Times ◽  
Heavy Tailed

AbstractWe consider the Δ(i)/G/1 queue, in which a total ofncustomers join a single-server queue for service. Customers join the queue independently after exponential times. We considerheavy-tailedservice-time distributions with tails decaying asx-α, α ∈ (1, 2). We consider the asymptotic regime in which the population size grows to ∞ and establish that the scaled queue-length process converges to an α-stable process with a negative quadratic drift. We leverage this asymptotic result to characterize the head start that is needed to create a long period of uninterrupted activity (a busy period). The heavy-tailed service times should be contrasted with the case of light-tailed service times, for which a similar scaling limit arises (Betet al.(2015)), but then with a Brownian motion instead of an α-stable process.

The single-server queue with service depending on queue size and with the preemptive-resume last-come–first-served queue discipline

1987 ◽  
Vol 24 (3) ◽  
pp. 758-767 ◽  
Author(s):  
D. Fakinos
Keyword(s):  
Queueing System ◽  
Limiting Distribution ◽  
Single Server ◽  
Queue Size ◽  
Single Server Queue ◽  
Preemptive Resume ◽  
Server Queue ◽  
Queue Discipline ◽  
Service Times

This paper studies the GI/G/1 queueing system assuming that customers have service times depending on the queue size and also that they are served in accordance with the preemptive-resume last-come–first-served queue discipline. Expressions are given for the limiting distribution of the queue size and the remaining durations of the corresponding services, when the system is considered at arrival epochs, at departure epochs and continuously in time. Also these results are applied to some particular cases of the above queueing system.

The single server queue with Poisson input and semi-Markov service times

1966 ◽  
Vol 3 (1) ◽  
pp. 202-230 ◽  
Author(s):  
Marcel F. Neuts
Keyword(s):  
Markov Process ◽  
Time Dependence ◽  
Stationary Solutions ◽  
Single Server ◽  
Single Server Queue ◽  
Poisson Input ◽  
Server Queue ◽  
Semi Markov Process ◽  
Poisson Arrivals ◽  
Service Times

We assume that the successive service times in a single server queue with Poisson arrivals form an m-state semi-Markov process.The results for the M/G/1 queue are extended to this case. Both the time-dependence and the stationary solutions are discussed.

On the distribution of queueing times

1953 ◽  
Vol 49 (3) ◽  
pp. 449-461 ◽  
Author(s):  
Walter L. Smith
Keyword(s):  
Single Server ◽  
Theoretical Studies ◽  
Single Server Queue ◽  
Hypothetical Model ◽  
Arrival Times ◽  
Present Treatment ◽  
Server Queue ◽  
Service Times

The hypothetical model that we shall be considering in this paper is referred to as the single-server queue, and the details of this model are given in a recent paper by Lindley(5). The present treatment involves exactly the same assumptions as Lindley has given already, and we refer to his paper for a rigorous statement of them. Briefly, we shall be assuming general independent service times and general independent input or arrival times. Theoretical studies of the single-server queue are capable of wide applications, many of which are described in a paper by Kendall (4) and in the discussion to that paper.

Logarithmic asymptotics for steady-state tail probabilities in a single-server queue

1994 ◽  
Vol 31 (A) ◽  
pp. 131-156 ◽  
Author(s):  
Peter W. Glynn ◽  
Ward Whitt
Keyword(s):  
Steady State ◽  
Decay Rate ◽  
Partial Sums ◽  
Asymptotic Result ◽  
Service Discipline ◽  
Single Server ◽  
Single Server Queue ◽  
Asymptotic Decay ◽  
Server Queue ◽  
Service Times

We consider the standard single-server queue with unlimited waiting space and the first-in first-out service discipline, but without any explicit independence conditions on the interarrival and service times. We find conditions for the steady-state waiting-time distribution to have asymptotics of the form x –1 log P(W > x) → –θ ∗as x → ∞for θ ∗ > 0. We require only stationarity of the basic sequence of service times minus interarrival times and a Gärtner–Ellis condition for the cumulant generating function of the associated partial sums, i.e. n –1 log E exp (θSn ) → ψ (θ) as n → ∞, plus regularity conditions on the decay rate function ψ. The asymptotic decay rate θ is the root of the equation ψ (θ) = 0. This result in turn implies a corresponding asymptotic result for the steady-state workload in a queue with general non-decreasing input. This asymptotic result covers the case of multiple independent sources, so that it provides additional theoretical support for a concept of effective bandwidths for admission control in multiclass queues based on asymptotic decay rates.

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