Investigation of the mean waiting time for queueing system with many servers

1969 ◽  
Vol 21 (1) ◽  
pp. 357-366 ◽  
Author(s):  
Toji Makino
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Mean Waiting Time ◽  
The Mean

The general N server finite queue

1971 ◽  
Vol 8 (04) ◽  
pp. 828-834 ◽  
Author(s):  
Asha Seth Kapadia
Keyword(s):  
Waiting Time ◽  
Busy Period ◽  
Queueing System ◽  
List Type ◽  
Type Number ◽  
Stochastic Nature ◽  
Mean Waiting Time ◽  
Queue Discipline ◽  
Mean And Variance ◽  
The Mean

Kingman (1962) studied the effect of queue discipline on the mean and variance of the waiting time. He made no assumptions regarding the stochastic nature of the input and the service distributions, except that the input and service processes are independent of each other. When the following two conditions hold: (a) no server sits idle while there are customers waiting to be served; (b) the busy period is finite with probability one (i.e., the queue empties infinitely often with probability one); he has shown that the mean waiting time is independent of the queue discipline and the variance of the waiting time is a minimum when the customers are served in order of their arrival. Conditions (a) and (b) will henceforward be called Kingman conditions and a queueing system satisfying Kingman conditions will be referred to in the text as a Kingman queue.

On a property of the variance of the waiting time of a queue

1968 ◽  
Vol 5 (3) ◽  
pp. 702-703 ◽  
Author(s):  
D. G. Tambouratzis
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Mean Waiting Time ◽  
Queue Discipline ◽  
The Mean ◽  
Number Of Customers

In this note, we consider a queueing system under any discipline which does not affect the distribution of the number of customers in the queue at any time. We shall show that the variance of the waiting time is a maximum when the queue discipline is “last come, first served”. This result complements that of Kingman [1] who showed that, under the same assumptions, the mean waiting time is independent of the queue discipline and the variance of the waiting time is a minimum when the customers are served in the order of their arrival.

scholarly journals Delay Analysis of anM/G/1/KPriority Queueing System with Push-out Scheme

2007 ◽  
Vol 2007 ◽  
pp. 1-12 ◽  
Author(s):  
Yutae Lee ◽  
Bong Dae Choi ◽  
Bara Kim ◽  
Dan Keun Sung
Keyword(s):  
Communication Networks ◽  
Waiting Time ◽  
Queueing System ◽  
Waiting Times ◽  
Loss Probability ◽  
Mean Waiting Time ◽  
The Mean ◽  
Recursive Equations ◽  
Push Out ◽  
Stieltjes Transforms

This paper considers anM/G/1/Kqueueing system with push-out scheme which is one of the loss priority controls at a multiplexer in communication networks. The loss probability for the model with push-out scheme has been analyzed, but the waiting times are not available for the model. Using a set of recursive equations, this paper derives the Laplace-Stieltjes transforms (LSTs) of the waiting time and the push-out time of low-priority messages. These results are then utilized to derive the loss probability of each traffic type and the mean waiting time of high-priority messages. Finally, some numerical examples are provided.

The general N server finite queue

1971 ◽  
Vol 8 (4) ◽  
pp. 828-834 ◽  
Author(s):  
Asha Seth Kapadia
Keyword(s):  
Waiting Time ◽  
Busy Period ◽  
Queueing System ◽  
List Type ◽  
Type Number ◽  
Stochastic Nature ◽  
Mean Waiting Time ◽  
Queue Discipline ◽  
Mean And Variance ◽  
The Mean

Kingman (1962) studied the effect of queue discipline on the mean and variance of the waiting time. He made no assumptions regarding the stochastic nature of the input and the service distributions, except that the input and service processes are independent of each other. When the following two conditions hold: (a)no server sits idle while there are customers waiting to be served;(b)the busy period is finite with probability one (i.e., the queue empties infinitely often with probability one); he has shown that the mean waiting time is independent of the queue discipline and the variance of the waiting time is a minimum when the customers are served in order of their arrival. Conditions (a) and (b) will henceforward be called Kingman conditions and a queueing system satisfying Kingman conditions will be referred to in the text as a Kingman queue.

On a property of the variance of the waiting time of a queue

1968 ◽  
Vol 5 (03) ◽  
pp. 702-703 ◽  
Author(s):  
D. G. Tambouratzis
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Mean Waiting Time ◽  
Queue Discipline ◽  
The Mean ◽  
Number Of Customers

In this note, we consider a queueing system under any discipline which does not affect the distribution of the number of customers in the queue at any time. We shall show that the variance of the waiting time is a maximum when the queue discipline is “last come, first served”. This result complements that of Kingman [1] who showed that, under the same assumptions, the mean waiting time is independent of the queue discipline and the variance of the waiting time is a minimum when the customers are served in the order of their arrival.

scholarly journals Analysis of MAP/PH(1), PH(2)/2 Queue with Bernoulli Vacations

2008 ◽  
Vol 2008 ◽  
pp. 1-20 ◽  
Author(s):  
B. Krishna Kumar ◽  
R. Rukmani ◽  
V. Thangaraj
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Queueing System ◽  
Arrival Process ◽  
Waiting Time Distribution ◽  
Steady State Probability ◽  
Matrix Geometric Method ◽  
Mean Waiting Time ◽  
The Mean ◽  
Number Of Customers

We consider a two-heterogeneous-server queueing system with Bernoulli vacation in which customers arrive according to a Markovian arrival process (MAP). Servers returning from vacation immediately take another vacation if no customer is waiting. Using matrix-geometric method, the steady-state probability of the number of customers in the system is investigated. Some important performance measures are obtained. The waiting time distribution and the mean waiting time are also discussed. Finally, some numerical illustrations are provided.

scholarly journals A queueing model for error control of partial buffer sharing in ATM

1999 ◽  
Vol 5 (4) ◽  
pp. 329-348
Author(s):  
Boo Yong Ahn ◽  
Ho Woo Lee
Keyword(s):  
Error Control ◽  
Approximation Scheme ◽  
Queueing System ◽  
Recursive Method ◽  
Loss Probabilities ◽  
Mean Waiting Time ◽  
System Equations ◽  
The Mean ◽  
Buffer Sharing

We model the error control of the partial buffer sharing of ATM by a queueing systemM1,M2/G/1/K+1with threshold and instantaneous Bernoulli feedback. We first derive the system equations and develop a recursive method to compute the loss probabilities at an arbitrary time epoch. We then build an approximation scheme to compute the mean waiting time of each class of cells. An algorithm is developed for finding the optimal threshold and queue capacity for a given quality of service.

scholarly journals Estimation of the mean waiting time of a customer subject to balking: a simulation study

2007 ◽  
Vol 19 (1) ◽  
pp. 63-63
Author(s):  
Jaejin Jang ◽  
Jaewoo Chung ◽  
Jungdae Suh ◽  
Jongtae Rhee
Keyword(s):  
Waiting Time ◽  
Simulation Study ◽  
Mean Waiting Time ◽  
The Mean

scholarly journals Waiting Time Problems for Patterns in a Sequence of Multi-State Trials

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1893
Author(s):  
Bara Kim ◽  
Jeongsim Kim ◽  
Jerim Kim
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Probability Generating Function ◽  
Finite Collection ◽  
Numerical Inversion ◽  
Analytic Method ◽  
Waiting Time Distribution ◽  
Mean Waiting Time ◽  
The Matrix ◽  
The Mean

In this paper, we investigate waiting time problems for a finite collection of patterns in a sequence of independent multi-state trials. By constructing a finite GI/M/1-type Markov chain with a disaster and then using the matrix analytic method, we can obtain the probability generating function of the waiting time. From this, we can obtain the stopping probabilities and the mean waiting time, but it also enables us to compute the waiting time distribution by a numerical inversion.

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