An analytical method for the calculation of the waiting time distribution of a discrete time G/G/1-queueing system with batch arrivals

OR Spectrum ◽  
2006 ◽  
Vol 29 (4) ◽  
pp. 745-763 ◽  
Author(s):  
Marc Schleyer ◽  
Kai Furmans
Keyword(s):  
Discrete Time ◽  
Waiting Time ◽  
Analytical Method ◽  
Time Distribution ◽  
Queueing System ◽  
Waiting Time Distribution ◽  
Batch Arrivals

scholarly journals The waiting time analysis of a discrete-time queue with arrivals as a discrete autoregressive process of order 1

2002 ◽  
Vol 39 (03) ◽  
pp. 619-629 ◽  
Author(s):  
Gang Uk Hwang ◽  
Bong Dae Choi ◽  
Jae-Kyoon Kim
Keyword(s):  
Discrete Time ◽  
Waiting Time ◽  
Time Distribution ◽  
Heavy Traffic ◽  
Autoregressive Process ◽  
Waiting Time Distribution ◽  
Tail Probabilities ◽  
Waiting Time Distributions ◽  
Virtual Waiting Time ◽  
Asymptotic Decay Rate

We consider a discrete-time queueing system with the discrete autoregressive process of order 1 (DAR(1)) as an input process and obtain the actual waiting time distribution and the virtual waiting time distribution. As shown in the analysis, our approach provides a natural numerical algorithm to compute the waiting time distributions, based on the theory of the GI/G/1 queue, and consequently we can easily investigate the effect of the parameters of the DAR(1) on the waiting time distributions. We also derive a simple approximation of the asymptotic decay rate of the tail probabilities for the virtual waiting time in the heavy traffic case.

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.

Waiting-Time Percentiles in the Multi-server Mx/G/c Queue with Batch Arrivals

1987 ◽  
Vol 1 (1) ◽  
pp. 75-96 ◽  
Author(s):  
A. M. Eikeboom ◽  
H. C. Tijms
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Linear Interpolation ◽  
Service Time Distribution ◽  
Waiting Time Distribution ◽  
Batch Arrivals ◽  
Special Cases ◽  
Moment Approximation ◽  
Multi Server ◽  
Validation Experiments

This paper deals with the MX/G/c queue. Using analytical results for the special cases of the MX/M/c queue and the MX/D/c queue, a two-moment approximation is proposed for the waiting-time percentiles in the general case. This approximation is based on a linear interpolation with respect to the squared coefficient of variation of the service time distribution. Validation experiments indicate that this approximation performs quite well for practical purposes. In particular, the practically important percentiles in the tail of the waiting-time distribution are approximated extremely well.

Waiting Time in M/G/1 Queues with Impolite Arrival Disciplines

1995 ◽  
Vol 9 (2) ◽  
pp. 255-267 ◽  
Author(s):  
Süleyman Òzekici ◽  
Jingwen Li ◽  
Fee Seng Chou
Keyword(s):  
Performance Measures ◽  
Waiting Time ◽  
Time Distribution ◽  
Iterative Procedure ◽  
Queueing System ◽  
Waiting Time Distribution ◽  
Special Model ◽  
Average Waiting Time ◽  
Random Position ◽  
Number Of Customers

We consider a queueing system where arriving customers join the queue at some random position. This constitutes an impolite arrival discipline because customers do not necessarily go to the end of the line upon arrival. Although mean performance measures like the average waiting time and average number of customers in the queue are the same for all such disciplines, we show that the variance of the waiting time increases as the arrival discipline becomes more impolite, in the sense that a customer is more likely to choose a position closer to the server. For the M/G/1 model, we also provide an iterative procedure for computing the moments of the waiting time distribution. Explicit computational formulas are derived for an interesting special model where a customer joins the queue either at the head or at the end of the line.

An extension of the waiting time distribution of first conceptions

1978 ◽  
Vol 10 (3) ◽  
pp. 231-234
Author(s):  
K. B. Pathak
Keyword(s):  
Discrete Time ◽  
Waiting Time ◽  
Time Distribution ◽  
Probability Model ◽  
Waiting Time Distribution ◽  
Moment Estimates ◽  
The Moment

SummaryA discrete time probability model has been developed to describe the waiting time until the first conception for a woman who is married before the age of 20 years. The model is illustrated by applying it to data on the time of first conception on the basis of the moment estimates of the parameters.

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