On Mean Return Time in Queueing System with Constant Service Time and Bi-level Hysteric Policy

2013 ◽  
pp. 11-19 ◽  
Author(s):  
Pavel Abaev ◽  
Alexander Pechinkin ◽  
Rostislav Razumchik
Keyword(s):  
Service Time ◽  
Queueing System ◽  
Return Time

scholarly journals Queueing system H2|GI|<» with an infinite mean of service time

2018 ◽  
pp. 72-83
Author(s):  
Anatoly Andreevich Nazarov ◽  
◽  
Ekaterina Evgenievna Khudyashova ◽  
Alexander Nikolaevich Moiseev
Keyword(s):  
Service Time ◽  
Queueing System

On the waiting time distribution in a generalized queueing system with uniformly bounded sojourn times

1972 ◽  
Vol 9 (3) ◽  
pp. 642-649 ◽  
Author(s):  
Jacqueline Loris-Teghem
Keyword(s):  
Generating Function ◽  
Waiting Time ◽  
Service Time ◽  
Time Distribution ◽  
Queueing System ◽  
Waiting Time Distribution ◽  
Stieltjes Transform ◽  
Sojourn Times ◽  
Stieltjes Transforms ◽  
Uniformly Bounded

A generalized queueing system with (N + 2) types of triplets (delay, service time, probability of joining the queue) and with uniformly bounded sojourn times is considered. An expression for the generating function of the Laplace-Stieltjes transforms of the waiting time distributions is derived analytically, in a case where some of the random variables defining the model have a rational Laplace-Stieltjes transform.The standard Kl/Km/1 queueing system with uniformly bounded sojourn times is considered in particular.

On a property of a refusals stream

1997 ◽  
Vol 34 (03) ◽  
pp. 800-805 ◽  
Author(s):  
Vyacheslav M. Abramov
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Busy Period ◽  
Elementary Proof ◽  
Queueing System ◽  
Queueing Systems ◽  
Single Server ◽  
Wide Family

This paper consists of two parts. The first part provides a more elementary proof of the asymptotic theorem of the refusals stream for an M/GI/1/n queueing system discussed in Abramov (1991a). The central property of the refusals stream discussed in the second part of this paper is that, if the expectations of interarrival and service time of an M/GI/1/n queueing system are equal to each other, then the expectation of the number of refusals during a busy period is equal to 1. This property is extended for a wide family of single-server queueing systems with refusals including, for example, queueing systems with bounded waiting time.

scholarly journals On the starshapeness of G/G/c queueing systems

1991 ◽  
Vol 23 (2) ◽  
pp. 431-435 ◽  
Author(s):  
J. George Shanthikumar ◽  
Couchen Wu
Keyword(s):  
Service Time ◽  
Queueing System ◽  
Queueing Systems ◽  
Single Stage ◽  
Sojourn Times ◽  
Optimal Service ◽  
The Mean

In this paper we show that the waiting and the sojourn times of a customer in a single-stage, multiple-server, G/G/c queueing system are increasing and starshaped with respect to the mean service time. Usefulness of this result in the design of the optimal service speed in the G/G/c queueing system is also demonstrated.

On extremal service disciplines in single-stage queueing systems

1990 ◽  
Vol 27 (02) ◽  
pp. 409-416 ◽  
Author(s):  
Rhonda Righter ◽  
J. George Shanthikumar ◽  
Genji Yamazaki
Keyword(s):  
Service Time ◽  
Sojourn Time ◽  
Queueing System ◽  
Residual Life ◽  
Queueing Systems ◽  
Mean Residual Life ◽  
Service Discipline ◽  
Service Time Distribution ◽  
Service Disciplines ◽  
Number Of Customers

It is shown that among all work-conserving service disciplines that are independent of the future history, the first-come-first-served (FCFS) service discipline minimizes [maximizes] the average sojourn time in a G/GI/1 queueing system with new better [worse] than used in expectation (NBUE[NWUE]) service time distribution. We prove this result using a new basic identity of G/GI/1 queues that may be of independent interest. Using a relationship between the workload and the number of customers in the system with different lengths of attained service it is shown that the average sojourn time is minimized [maximized] by the least-attained-service time (LAST) service discipline when the service time has the decreasing [increasing] mean residual life (DMRL[IMRL]) property.

Functional limit theorems for the queue GI/G/1 in light traffic

1971 ◽  
Vol 3 (02) ◽  
pp. 269-281 ◽  
Author(s):  
Donald L. Iglehart
Keyword(s):  
Service Time ◽  
Limit Theorems ◽  
Queueing System ◽  
Deterministic System ◽  
Traffic Intensity ◽  
Random Vectors ◽  
Functional Limit ◽  
Light Traffic ◽  
Functional Limit Theorems ◽  
Natural Measure

We consider a single GI/G/1 queueing system in which customer number 0 arrives at time t 0 = 0, finds a free server, and experiences a service time v 0. The nth customer arrives at time t n and experiences a service time v n . Let the interarrival times t n - t n-1 = u n , n ≧ 1, and define the random vectors X n = (v n-1, u n ), n ≧ 1. We assume the sequence of random vectors {X n : n ≧ 1} is independent and identically distributed (i.i.d.). Let E{u n } = λ-1 and E{v n } = μ-1, where 0 &lt; λ, μ &lt; ∞. In addition, we shall always assume that E{v 0 2} &lt; ∞ and that the deterministic system in which both v n and u n are degenerate is excluded. The natural measure of congestion for this system is the traffic intensity ρ = λ/μ. In this paper we shall restrict our attention to systems in which ρ &lt; 1. Under this condition, which we shall refer to as light traffic, our system is of course stable.

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