scholarly journals Stationary Waiting-Time Distributions for Single-Server Queues

1962 ◽  
Vol 33 (4) ◽  
pp. 1323-1339 ◽  
Author(s):  
R. M. Loynes
Keyword(s):  
Waiting Time ◽  
Single Server ◽  
Waiting Time Distributions ◽  
Single Server Queues ◽  
Stationary Waiting Time

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.

Stationary waiting-time distributions in the GI/PH/1 queue

1981 ◽  
Vol 18 (4) ◽  
pp. 901-912 ◽  
Author(s):  
Marcel F. Neuts
Keyword(s):  
Waiting Time ◽  
Embedded Markov Chain ◽  
Asymptotic Results ◽  
Waiting Time Distributions ◽  
Structured Systems ◽  
Queue Discipline ◽  
The Matrix ◽  
Constant Coefficients ◽  
Linear Differential ◽  
Stationary Waiting Time

It is known that the stable GI/PH/1 queue has an embedded Markov chain whose invariant probability vector is matrix-geometric with a rate matrix R. In terms of the matrix R, the stationary waiting-time distributions at arrivals, at an arbitrary time point and until the customer's departure may be evaluated by solving finite, highly structured systems of linear differential equations with constant coefficients. Asymptotic results, useful in truncating the computations, are also obtained. The queue discipline is first-come, first-served.

A new approach to the G/G/1 queue with generalized setup time and exhaustive service

1994 ◽  
Vol 31 (4) ◽  
pp. 1083-1097 ◽  
Author(s):  
Huan Li ◽  
Yixin Zhu
Keyword(s):  
Waiting Time ◽  
Queueing Systems ◽  
Recursive Formula ◽  
Setup Time ◽  
Stochastic Decomposition ◽  
Single Server ◽  
New Approach ◽  
Service Interruption ◽  
Special Cases ◽  
Stationary Waiting Time

We consider a class of G/G/1 queueing models with independent generalized setup time and exhaustive service. It is shown that a variety of single-server queueing systems with service interruption are special cases of our model. We give a simple computational scheme for the moments of the stationary waiting time and sojourn time. Our numerical investigations indicate that the algorithm is quite accurate and fast in general. For the M/G/1 case, we are able to derive a recursive formula for the moments of the stationary waiting time, which includes the Takács formula as a special case. It immediately results in the stochastic decompòsition property which can be found in the literature.

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.

A new approach to the G/G/1 queue with generalized setup time and exhaustive service

1994 ◽  
Vol 31 (04) ◽  
pp. 1083-1097
Author(s):  
Huan Li ◽  
Yixin Zhu
Keyword(s):  
Waiting Time ◽  
Queueing Systems ◽  
Recursive Formula ◽  
Setup Time ◽  
Stochastic Decomposition ◽  
Single Server ◽  
New Approach ◽  
Service Interruption ◽  
Special Cases ◽  
Stationary Waiting Time

We consider a class of G/G/1 queueing models with independent generalized setup time and exhaustive service. It is shown that a variety of single-server queueing systems with service interruption are special cases of our model. We give a simple computational scheme for the moments of the stationary waiting time and sojourn time. Our numerical investigations indicate that the algorithm is quite accurate and fast in general. For the M/G/1 case, we are able to derive a recursive formula for the moments of the stationary waiting time, which includes the Takács formula as a special case. It immediately results in the stochastic decompòsition property which can be found in the literature.

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