scholarly journals Transient Analysis of Two-Dimensional State M/G/1 Queueing Model with Multiple Vacations and Bernoulli Schedule

2012 ◽  
Vol 40 (13) ◽  
pp. 17-22
Author(s):  
Indra Indra ◽  
Renu Renu
Keyword(s):  
Transient Analysis ◽  
Queueing Model ◽  
Two Dimensional ◽  
Multiple Vacations ◽  
Bernoulli Schedule

scholarly journals Zero Queueing for Multi-Server Jobs

2021 ◽  
Vol 5 (1) ◽  
pp. 1-25
Author(s):  
Weina Wang ◽  
Qiaomin Xie ◽  
Mor Harchol-Balter
Keyword(s):  
Cloud Computing ◽  
Stability Region ◽  
Transient Analysis ◽  
Queueing Systems ◽  
Sufficient Conditions ◽  
Hard Problem ◽  
Queueing Model ◽  
Multiple Servers ◽  
First Results ◽  
Multi Server

Cloud computing today is dominated by multi-server jobs. These are jobs that request multiple servers simultaneously and hold onto all of these servers for the duration of the job. Multi-server jobs add a lot of complexity to the traditional one-server-per-job model: an arrival might not "fit'' into the available servers and might have to queue, blocking later arrivals and leaving servers idle. From a queueing perspective, almost nothing is understood about multi-server job queueing systems; even understanding the exact stability region is a very hard problem. In this paper, we investigate a multi-server job queueing model under scaling regimes where the number of servers in the system grows. Specifically, we consider a system with multiple classes of jobs, where jobs from different classes can request different numbers of servers and have different service time distributions, and jobs are served in first-come-first-served order. The multi-server job model opens up new scaling regimes where both the number of servers that a job needs and the system load scale with the total number of servers. Within these scaling regimes, we derive the first results on stability, queueing probability, and the transient analysis of the number of jobs in the system for each class. In particular we derive sufficient conditions for zero queueing. Our analysis introduces a novel way of extracting information from the Lyapunov drift, which can be applicable to a broader scope of problems in queueing systems.

scholarly journals Fluid Queue Driven by anM/M/1Queue Subject to Bernoulli-Schedule-Controlled Vacation and Vacation Interruption

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Kolinjivadi Viswanathan Vijayashree ◽  
Atlimuthu Anjuka
Keyword(s):  
Death Process ◽  
Queueing Model ◽  
Fluid Queue ◽  
Stationary Analysis ◽  
Governing System ◽  
Matrix Geometric Method ◽  
Vacation Interruption ◽  
Model Subject ◽  
Steady State Probabilities ◽  
Bernoulli Schedule

This paper deals with the stationary analysis of a fluid queue driven by anM/M/1queueing model subject to Bernoulli-Schedule-Controlled Vacation and Vacation Interruption. The model under consideration can be viewed as a quasi-birth and death process. The governing system of differential difference equations is solved using matrix-geometric method in the Laplacian domain. The resulting solutions are then inverted to obtain an explicit expression for the joint steady state probabilities of the content of the buffer and the state of the background queueing model. Numerical illustrations are added to depict the convergence of the stationary buffer content distribution to one subject to suitable stability conditions.

Transient analysis of M/M/1 queues in discrete time by general server vacations

1994 ◽  
Vol 31 (A) ◽  
pp. 115-129 ◽  
Author(s):  
W. Böhm ◽  
S. G. Mohanty
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Transient Analysis ◽  
Queueing System ◽  
Queueing Model ◽  
Discrete Parameter ◽  
Server Vacations ◽  
Special Case ◽  
Combinatorial Methods ◽  
Transient And Steady State

In this contribution we consider an M/M/1 queueing model with general server vacations. Transient and steady state analysis are carried out in discrete time by combinatorial methods. Using weak convergence of discrete-parameter Markov chains we also obtain formulas for the corresponding continuous-time queueing model. As a special case we discuss briefly a queueing system with a T-policy operating.

Transient Analysis of a Two-Heterogeneous Severs Queue with Impatient Behaviour and Multiple Vacations

2018 ◽  
Vol 6 (1) ◽  
pp. 69-84
Author(s):  
Jia Xu ◽  
Liwei Liu ◽  
Taozeng Zhu
Keyword(s):  
Generating Functions ◽  
Transient Analysis ◽  
Bessel Functions ◽  
Queueing System ◽  
System Size ◽  
Heterogeneous Servers ◽  
Modified Bessel Functions ◽  
Multiple Vacations ◽  
Special Cases ◽  
Mean And Variance

AbstractWe consider anM/M/2 queueing system with two-heterogeneous servers and multiple vacations. Customers arrive according to a Poisson process. However, customers become impatient when the system is on vacation. We obtain explicit expressions for the time dependent probabilities, mean and variance of the system size at timetby employing probability generating functions, continued fractions and properties of the modified Bessel functions. Finally, two special cases are provided.

Sign in / Sign up

Export Citation Format

Share Document