An approximation for the waiting time distribution in single server queues

1980 ◽  
Vol 27 (2) ◽  
pp. 223-230
Author(s):  
Irwin Greenberg
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Single Server Queues

Convex ordering of the attained waiting times in single-server queues and related problems

1991 ◽  
Vol 28 (02) ◽  
pp. 433-445 ◽  
Author(s):  
Masakiyo Miyazawa ◽  
Genji Yamazaki
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Waiting Times ◽  
Service Discipline ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Convex Order ◽  
Convex Ordering ◽  
Single Server Queues ◽  
Service Disciplines

The attained waiting time of customers in service of the G/G/1 queue is compared for various work-conserving service disciplines. It is proved that the attained waiting time distribution is minimized (maximized) in convex order when the discipline is FCFS (PR-LCFS). We apply the result to characterize finiteness of moments of the attained waiting time in the GI/GI/1 queue with an arbitrary work-conserving service discipline. In this discussion, some interesting relationships are obtained for a PR-LCFS queue.

Convex ordering of the attained waiting times in single-server queues and related problems

1991 ◽  
Vol 28 (2) ◽  
pp. 433-445
Author(s):  
Masakiyo Miyazawa ◽  
Genji Yamazaki
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Waiting Times ◽  
Service Discipline ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Convex Order ◽  
Convex Ordering ◽  
Single Server Queues ◽  
Service Disciplines

The attained waiting time of customers in service of the G/G/1 queue is compared for various work-conserving service disciplines. It is proved that the attained waiting time distribution is minimized (maximized) in convex order when the discipline is FCFS (PR-LCFS). We apply the result to characterize finiteness of moments of the attained waiting time in the GI/GI/1 queue with an arbitrary work-conserving service discipline. In this discussion, some interesting relationships are obtained for a PR-LCFS queue.

scholarly journals An M/G/1 queue with multiple types of feedback and gated vacations

1997 ◽  
Vol 34 (03) ◽  
pp. 773-784 ◽  
Author(s):  
Onno J. Boxma ◽  
Uri Yechiali
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Queue Length ◽  
Time Distribution ◽  
Single Server ◽  
Service Time Distribution ◽  
Waiting Time Distribution ◽  
Single Server Queue ◽  
Server Queue ◽  
Poisson Arrivals

This paper considers a single-server queue with Poisson arrivals and multiple customer feedbacks. If the first service attempt of a newly arriving customer is not successful, he returns to the end of the queue for another service attempt, with a different service time distribution. He keeps trying in this manner (as an ‘old' customer) until his service is successful. The server operates according to the ‘gated vacation' strategy; when it returns from a vacation to find K (new and old) customers, it renders a single service attempt to each of them and takes another vacation, etc. We study the joint queue length process of new and old customers, as well as the waiting time distribution of customers. Some extensions are also discussed.

Stochastic bounds for the single-server queue

1976 ◽  
Vol 80 (3) ◽  
pp. 521-525 ◽  
Author(s):  
J. Köllerström
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Infinite Divisibility ◽  
Single Server ◽  
Traffic Intensity ◽  
Waiting Time Distribution ◽  
Single Server Queue ◽  
Exponential Tail ◽  
Server Queue ◽  
Fitting In

Various elegant properties have been found for the waiting time distribution G for the queue GI/G/1 in statistical equilibrium, such as infinite divisibility ((1), p. 282) and that of having an exponential tail ((11), (2), p. 411, (1), p. 324). Here we derive another property which holds quite generally, provided the traffic intensity ρ < 1, and which is extremely simple, fitting in with the above results as well as yielding some useful properties in the form of upper and lower stochastic bounds for G which augment the bounds obtained by Kingman (5), (6), (8) and by Ross (10).

scholarly journals Identification of waiting time distribution ofM/G/1,Mx/G/1,GIr/M/1queueing systems

1988 ◽  
Vol 11 (3) ◽  
pp. 589-597
Author(s):  
A. Ghosal ◽  
S. Madan
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Queueing System ◽  
Numerical Study ◽  
Queueing Models ◽  
Single Server ◽  
Waiting Time Distribution ◽  
System A ◽  
Bulk Arrival

This paper brings out relations among the moments of various orders of the waiting time of the1st customer and a randomly selected customer of an arrival group for bulk arrivals queueing models, and as well as moments of the waiting time (in queue) forM/G/1queueing system. A numerical study of these relations has been developed in order to find the(β1,β2)measures of waiting time distribution in a comutable form. On the basis of these measures one can look into the nature of waiting time distribution of bulk arrival queues and the single serverM/G/1queue.

Exponential approximation of waiting time and queue size for queues in heavy traffic

1990 ◽  
Vol 22 (1) ◽  
pp. 230-240 ◽  
Author(s):  
Władysław Szczotka
Keyword(s):  
Waiting Time ◽  
Wide Class ◽  
Time Distribution ◽  
Heavy Traffic ◽  
Single Server ◽  
Queue Size ◽  
Exponential Approximation ◽  
Waiting Time Distribution ◽  
Stationary Waiting Time ◽  
Stationary Representation

An exponential approximation for the stationary waiting time distribution and the stationary queue size distribution for single-server queues in heavy traffic is given for a wide class of queues. This class contains for example not only queues for which the generic sequence, i.e. the sequence of service times and interarrival times, is stationary but also such queues for which the generic sequence is asymptotically stationary in some sense. The conditions ensuring the exponential approximation of the characteristics considered in heavy traffic are expressed in terms of the invariance principle for the stationary representation of the generic sequence and its first two moments.

Exponential approximation of waiting time and queue size for queues in heavy traffic

1990 ◽  
Vol 22 (01) ◽  
pp. 230-240 ◽  
Author(s):  
Władysław Szczotka
Keyword(s):  
Waiting Time ◽  
Wide Class ◽  
Time Distribution ◽  
Heavy Traffic ◽  
Single Server ◽  
Queue Size ◽  
Exponential Approximation ◽  
Waiting Time Distribution ◽  
Stationary Waiting Time ◽  
Stationary Representation

An exponential approximation for the stationary waiting time distribution and the stationary queue size distribution for single-server queues in heavy traffic is given for a wide class of queues. This class contains for example not only queues for which the generic sequence, i.e. the sequence of service times and interarrival times, is stationary but also such queues for which the generic sequence is asymptotically stationary in some sense. The conditions ensuring the exponential approximation of the characteristics considered in heavy traffic are expressed in terms of the invariance principle for the stationary representation of the generic sequence and its first two moments.

scholarly journals Single-server queueing systems with uniformly limited queueing time

1964 ◽  
Vol 4 (4) ◽  
pp. 489-505 ◽  
Author(s):  
D. J. Daley
Keyword(s):  
Integral Equation ◽  
Waiting Time ◽  
Time Distribution ◽  
Busy Period ◽  
Queueing System ◽  
Queueing Systems ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Loss Distribution ◽  
Queueing Time

SummaryThe paper considers the queueing system GI/G/1 with a type of customer impatience, namely, that the total queueing-time is uniformly limited. Using Lindiley's approach [10], an integral equation for the limiting waiting- time distribution is derived, and this is solved explicitly for M/G/1 using an expansion of the Pollaczek-Khintchine formula. It is also solved, in principle for Ej/G/l, and explicitly for Ej/Ek/l. A duality noted between GIA(x)/GB(x)/l and GIB(x)/GA(x)/l relates solutions for GI/Ek/l to Ek/G/l. Finally the equation for the busy period in GI/G/l is derived and related to the no-customer-loss distribution and dual distributions.

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