scholarly journals M/M/1 Multiple Vacation Queueing Systems With Differentiated Vacations and Vacation Interruptions

IEEE Access ◽  
2014 ◽  
Vol 2 ◽  
pp. 1384-1395 ◽  
Author(s):  
Olubukola A. Isijola-Adakeja ◽  
Oliver C. Ibe
Keyword(s):  
Queueing Systems ◽  
Multiple Vacation

scholarly journals On a first passage problem in general queueing systems with multiple vacations

1992 ◽  
Vol 5 (2) ◽  
pp. 177-192 ◽  
Author(s):  
Jewgeni H. Dshalalow
Keyword(s):  
Preliminary Analysis ◽  
Queueing System ◽  
Queueing Systems ◽  
Compound Poisson Process ◽  
Single Server ◽  
New Techniques ◽  
Queueing Process ◽  
Multiple Vacation ◽  
State Dependent ◽  
First Passage Problem

The author studies a generalized single-server queueing system with bulk arrivals and batch service, where the server takes vacations each time the queue level falls below r(≥1) in accordance with the multiple vacation discipline. The input to the system is assumed to be a compound Poisson process modulated by the system and the service is assumed to be state dependent. One of the essential part in the analysis of the system is the employment of new techniques related to the first excess level processes. A preliminary analysis of such processes and recent results of the author on modulated processes enabled the author to obtain all major characteristics for the queueing process explicitly. Various examples and applications are discussed.

scholarly journals On finite capacity queueing systems with a general vacation policy

2000 ◽  
Vol 13 (4) ◽  
pp. 411-414 ◽  
Author(s):  
Jacqueline Loris-Teghem
Keyword(s):  
Operations Research ◽  
Queue Length ◽  
Queueing System ◽  
Queueing Systems ◽  
Finite Capacity ◽  
Multiple Vacation ◽  
Poisson Arrival ◽  
Stationary Queue Length

We consider a Poisson arrival queueing system with finite capacity and a general vacation policy as described in Loris-Teghem [Queueing Systems 3 (1988), 41-52]. From our previous results regarding the stationary queue length distributions immediately after a departure and at an arbitrary epoch, we derive a relation between both distributions which extends a result given in Frey and Takahashi [Operations Research Letters 21 (1997), 95-100] for the particular case of an exhaustive service multiple vacation policy.

scholarly journals M/M/1 Multiple Vacation Queueing Systems with Differentiated Vacations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Oliver C. Ibe ◽  
Olubukola A. Isijola
Keyword(s):  
Steady State ◽  
Busy Period ◽  
Queueing System ◽  
Queueing Systems ◽  
Steady State Solution ◽  
State Solution ◽  
Multiple Vacation ◽  
Service Times

We consider a multiple vacation queueing system in which a vacation following a busy period has a different distribution from a vacation that is taken without serving at least one customer. For ease of analysis it is assumed that the service times are exponentially distributed and the two vacation types are also exponentially distributed but with different means. The steady-state solution is obtained.

OPTIMIZATION OF MARKOV SYSTEMS OF QUEUEING WITH WAITING TIME IN THE MATLAB SYSTEM

2017 ◽  
pp. 39-47
Author(s):  
Viktor Afonin ◽  
Vladimir Valer'evich Nikulin
Keyword(s):  
Queueing System ◽  
Queueing Systems ◽  
Random Variable ◽  
Model Systems ◽  
Queuing Systems ◽  
Input Flow ◽  
Continuous Random Variable ◽  
Input Stream ◽  
Time Intervals ◽  
Markov Systems

The article focuses on attempt to optimize two well-known Markov systems of queueing: a multichannel queueing system with finite storage, and a multichannel queueing system with limited queue time. In the Markov queuing systems, the intensity of the input stream of requests (requirements, calls, customers, demands) is subject to the Poisson law of the probability distribution of the number of applications in the stream; the intensity of service, as well as the intensity of leaving the application queue is subject to exponential distribution. In a Poisson flow, the time intervals between requirements are subject to the exponential law of a continuous random variable. In the context of Markov queueing systems, there have been obtained significant results, which are expressed in the form of analytical dependencies. These dependencies are used for setting up and numerical solution of the problem stated. The probability of failure in service is taken as a task function; it should be minimized and depends on the intensity of input flow of requests, on the intensity of service, and on the intensity of requests leaving the queue. This, in turn, allows to calculate the maximum relative throughput of a given queuing system. The mentioned algorithm was realized in MATLAB system. The results obtained in the form of descriptive algorithms can be used for testing queueing model systems during peak (unchanged) loads.

Cooperation in Queueing Systems

2020 ◽  
Author(s):  
Yaroslav Rosokha ◽  
Chen Wei
Keyword(s):  
Queueing Systems

scholarly journals Multipreconditioned GMRES for simulating stochastic automata networks

2018 ◽  
Vol 16 (1) ◽  
pp. 986-998
Author(s):  
Chun Wen ◽  
Ting-Zhu Huang ◽  
Xian-Ming Gu ◽  
Zhao-Li Shen ◽  
Hong-Fan Zhang ◽  
...  
Keyword(s):  
Steady State ◽  
Probability Distribution ◽  
Linear Systems ◽  
Iterative Methods ◽  
Communication Systems ◽  
Queueing Systems ◽  
Steady State Probability ◽  
Stochastic Automata ◽  
Automata Networks ◽  
Generator Matrices

AbstractStochastic Automata Networks (SANs) have a large amount of applications in modelling queueing systems and communication systems. To find the steady state probability distribution of the SANs, it often needs to solve linear systems which involve their generator matrices. However, some classical iterative methods such as the Jacobi and the Gauss-Seidel are inefficient due to the huge size of the generator matrices. In this paper, the multipreconditioned GMRES (MPGMRES) is considered by using two or more preconditioners simultaneously. Meanwhile, a selective version of the MPGMRES is presented to overcome the rapid increase of the storage requirements and make it practical. Numerical results on two models of SANs are reported to illustrate the effectiveness of these proposed methods.

scholarly journals A Taylor Series Approach for Service-Coupled Queueing Systems with Intermediate Load

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Ekaterina Evdokimova ◽  
Sabine Wittevrongel ◽  
Dieter Fiems
Keyword(s):  
Performance Measures ◽  
Queueing Systems ◽  
Poisson Processes ◽  
Series Expansions ◽  
Service Rate ◽  
Single Server ◽  
Queueing Model ◽  
State Space Explosion ◽  
Finite Queues ◽  
Service Rates

This paper investigates the performance of a queueing model with multiple finite queues and a single server. Departures from the queues are synchronised or coupled which means that a service completion leads to a departure in every queue and that service is temporarily interrupted whenever any of the queues is empty. We focus on the numerical analysis of this queueing model in a Markovian setting: the arrivals in the different queues constitute Poisson processes and the service times are exponentially distributed. Taking into account the state space explosion problem associated with multidimensional Markov processes, we calculate the terms in the series expansion in the service rate of the stationary distribution of the Markov chain as well as various performance measures when the system is (i) overloaded and (ii) under intermediate load. Our numerical results reveal that, by calculating the series expansions of performance measures around a few service rates, we get accurate estimates of various performance measures once the load is above 40% to 50%.

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