scholarly journals The effect of service time variability on maximum queue lengths in MX/G/1 queues

2005 ◽  
Vol 42 (03) ◽  
pp. 883-891
Author(s):  
Ger Koole ◽  
Misja Nuyens ◽  
Rhonda Righter
Keyword(s):  
Service Time ◽  
Queue Length ◽  
Busy Period ◽  
Random Variable ◽  
Buffer Size ◽  
Time Variability ◽  
Finite Buffer ◽  
Surprising Result ◽  
Maximum Queue Length ◽  
The Impact

We study the impact of service time distributions on the distribution of the maximum queue length during a busy period for the M X /G/1 queue. The maximum queue length is an important random variable to understand when designing the buffer size for finite-buffer (M/G/1/n) systems. We show the somewhat surprising result that, for three variations of the preemptive last-come–first-served discipline, the maximum queue length during a busy period is smaller when service times are more variable (in the convex sense).

scholarly journals The effect of service time variability on maximum queue lengths in MX/G/1 queues

2005 ◽  
Vol 42 (3) ◽  
pp. 883-891 ◽  
Author(s):  
Ger Koole ◽  
Misja Nuyens ◽  
Rhonda Righter
Keyword(s):  
Service Time ◽  
Queue Length ◽  
Busy Period ◽  
Random Variable ◽  
Buffer Size ◽  
Time Variability ◽  
Finite Buffer ◽  
Surprising Result ◽  
Maximum Queue Length ◽  
The Impact

We study the impact of service time distributions on the distribution of the maximum queue length during a busy period for the MX/G/1 queue. The maximum queue length is an important random variable to understand when designing the buffer size for finite-buffer (M/G/1/n) systems. We show the somewhat surprising result that, for three variations of the preemptive last-come–first-served discipline, the maximum queue length during a busy period is smaller when service times are more variable (in the convex sense).

scholarly journals On the Effect of Finite Buffer Truncation in a Two-Node Jackson Network

2005 ◽  
Vol 42 (01) ◽  
pp. 199-222 ◽  
Author(s):  
Yutaka Sakuma ◽  
Masakiyo Miyazawa
Keyword(s):  
Stability Condition ◽  
Queue Length ◽  
Length Distribution ◽  
Buffer Size ◽  
Finite Buffer ◽  
Jackson Network ◽  
Numerical Examples ◽  
Queue Length Distribution ◽  
Special Cases ◽  
The Stability

We consider a two-node Jackson network in which the buffer of node 1 is truncated. Our interest is in the limit of the tail decay rate of the queue-length distribution of node 2 when the buffer size of node 1 goes to infinity, provided that the stability condition of the unlimited network is satisfied. We show that there can be three different cases for the limit. This generalizes some recent results obtained for the tandem Jackson network. Special cases and some numerical examples are also presented.

The Trivariate Distribution of the Maximum Queue Length, the Number of Customers Served and the Duration of the Busy Period for the M/G/1 Queueing System

1969 ◽  
Vol 6 (1) ◽  
pp. 154-161 ◽  
Author(s):  
E.G. Enns
Keyword(s):  
Queue Length ◽  
Busy Period ◽  
Queueing System ◽  
Single Server ◽  
List Type ◽  
Type Number ◽  
Distribution Of The Maximum ◽  
Maximum Queue Length ◽  
Number Of Customers

In the study of the busy period for a single server queueing system, three variables that have been investigated individually or at most in pairs are:1.The duration of the busy period.2.The number of customers served during the busy period.3.The maximum number of customers in the queue during the busy period.

MODELING TRAFFIC FLOWS WITH QUEUEING MODELS: A REVIEW

2007 ◽  
Vol 24 (04) ◽  
pp. 435-461 ◽  
Author(s):  
TOM VAN WOENSEL ◽  
NICO VANDAELE
Keyword(s):  
Queueing Networks ◽  
Road Networks ◽  
Queueing Network ◽  
Analytical Application ◽  
Buffer Size ◽  
Queueing Models ◽  
Finite Buffer ◽  
Traffic Flows ◽  
Single Node ◽  
The Impact

In this paper, an overview of different analytic queueing models for traffic on road networks is presented. In the literature, it has been shown that queueing models can be used to adequately model uninterrupted traffic flows. This paper gives a broad review on this literature. Moreover, it is shown that the developed published methodologies (which are mainly single node oriented) can be extended towards queueing networks. First, an extension towards queueing networks with infinite buffer sizes is evaluated. Secondly, the assumption of infinite buffer sizes is dropped leading to queueing networks with finite buffer sizes. The impact of the buffer size when comparing the different queueing network methodologies is studied in detail. The paper ends with an analytical application tool to facilitate the optimal positioning of the counting points on a highway.

Algorithmic Analysis of the Maximum Queue Length in a Busy Period for theM/M/cRetrial Queue

2007 ◽  
Vol 19 (1) ◽  
pp. 121-126 ◽  
Author(s):  
Jesus R. Artalejo ◽  
Antonis Economou ◽  
M. J. Lopez-Herrero
Keyword(s):  
Queue Length ◽  
Busy Period ◽  
Maximum Queue Length ◽  
Algorithmic Analysis

scholarly journals On the Effect of Finite Buffer Truncation in a Two-Node Jackson Network

2005 ◽  
Vol 42 (1) ◽  
pp. 199-222 ◽  
Author(s):  
Yutaka Sakuma ◽  
Masakiyo Miyazawa
Keyword(s):  
Stability Condition ◽  
Queue Length ◽  
Length Distribution ◽  
Buffer Size ◽  
Finite Buffer ◽  
Jackson Network ◽  
Numerical Examples ◽  
Queue Length Distribution ◽  
Special Cases ◽  
The Stability

We consider a two-node Jackson network in which the buffer of node 1 is truncated. Our interest is in the limit of the tail decay rate of the queue-length distribution of node 2 when the buffer size of node 1 goes to infinity, provided that the stability condition of the unlimited network is satisfied. We show that there can be three different cases for the limit. This generalizes some recent results obtained for the tandem Jackson network. Special cases and some numerical examples are also presented.

scholarly journals Bounds for the variance of the busy period of the M/G/∞ queue

1984 ◽  
Vol 16 (4) ◽  
pp. 929-932 ◽  
Author(s):  
M. F. Ramalhoto
Keyword(s):  
Distribution Function ◽  
Lower Bounds ◽  
Service Time ◽  
Time Distribution ◽  
Busy Period ◽  
Random Variable ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Service Time Distribution ◽  
Lower And Upper Bounds

Some bounds for the variance of the busy period of an M/G/∞ queue are calculated as functions of parameters of the service-time distribution function. For any type of service-time distribution function, upper and lower bounds are evaluated in terms of the intensity of traffic and the coefficient of variation of the service time. Other lower and upper bounds are derived when the service time is a NBUE, DFR or IMRL random variable. The variance of the busy period is also related to the variance of the number of busy periods that are initiated in (0, t] by renewal arguments.

scholarly journals Bounds for the variance of the busy period of the M/G/∞ queue

1984 ◽  
Vol 16 (04) ◽  
pp. 929-932
Author(s):  
M. F. Ramalhoto
Keyword(s):  
Distribution Function ◽  
Lower Bounds ◽  
Service Time ◽  
Time Distribution ◽  
Busy Period ◽  
Random Variable ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Service Time Distribution ◽  
Lower And Upper Bounds

Some bounds for the variance of the busy period of an M/G/∞ queue are calculated as functions of parameters of the service-time distribution function. For any type of service-time distribution function, upper and lower bounds are evaluated in terms of the intensity of traffic and the coefficient of variation of the service time. Other lower and upper bounds are derived when the service time is a NBUE, DFR or IMRL random variable. The variance of the busy period is also related to the variance of the number of busy periods that are initiated in (0, t] by renewal arguments.

On the Busy Period of a Single Server Bulk Queue with a Modified Service Mechanism

1964 ◽  
Vol 13 (3-4) ◽  
pp. 163-171 ◽  
Author(s):  
U. Narayan Bhat
Keyword(s):  
Service Time ◽  
Queue Length ◽  
Busy Period ◽  
Single Server ◽  
Transient Behaviour ◽  
Bulk Queue ◽  
Poisson Arrivals

Summary The distribution of the busy period in a single server bulk queue with Poisson arrivals and a service mechanism providing for a different distribution for the first service time in a busy period is derived and a method of obtaining the transient behaviour of the queue length process is indicated.

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