Stationary distributions in a queueing system with vacation times and limited service

1989 ◽  
Vol 4 (1) ◽  
pp. 57-68 ◽  
Author(s):  
M. Kramer
Keyword(s):  
Queueing System ◽  
Stationary Distributions ◽  
Limited Service

scholarly journals M/G/1 vacation model with limited service discipline and hybrid switching-on policy

1997 ◽  
Vol 3 (3) ◽  
pp. 243-253
Author(s):  
Alexander V. Babitsky
Keyword(s):  
Generating Function ◽  
Busy Period ◽  
Optimization Problem ◽  
Queueing System ◽  
Service Discipline ◽  
Multiple Vacations ◽  
Queueing Process ◽  
Vacation Model ◽  
Hybrid Switching ◽  
Limited Service

The author studies an M/G/1 queueing system with multiple vacations. The server is turned off in accordance with the K-limited discipline, and is turned on in accordance with the T-N-hybrid policy. This is to say that the server will begin a vacation from the system if either the queue is empty orKcustomers were served during a busy period. The server idles until it finds at leastNwaiting units upon return from a vacation.Formulas for the distribution generating function and some characteristics of the queueing process are derived. An optimization problem is discussed.

GEOMETRIC-FORM BOUNDS FOR THE GIX/M/1 QUEUEING SYSTEM

1999 ◽  
Vol 13 (4) ◽  
pp. 509-520 ◽  
Author(s):  
Antonis Economou
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Queueing System ◽  
Embedded Markov Chain ◽  
Geometric Form ◽  
Stationary Distributions ◽  
Discrete Time Markov Chain ◽  
Numerical Studies ◽  
Simple Product

The GI/M/1 queueing system was long ago studied by considering the embedded discrete-time Markov chain at arrival epochs and was proved to have remarkably simple product-form stationary distributions both at arrival epochs and in continuous time. Although this method works well also in several variants of this system, it breaks down when customers arrive in batches. The resulting GIX/M/1 system has no tractable stationary distribution. In this paper we use a recent result of Miyazawa and Taylor (1997) to obtain a stochastic upper bound for the GIX/M/1 system. We also introduce a class of continuous-time Markov chains which are related to the original GIX/M/1 embedded Markov chain that are shown to have modified geometric stationary distributions. We use them to obtain easily computed stochastic lower bounds for the GIX/M/1 system. Numerical studies demonstrate the quality of these bounds.

QUASI-PRODUCT FORM TO A MULTINODE QUEUEING SYSTEM WITH A COMMON EXPONENTIAL SETUP SERVER

1999 ◽  
Vol 13 (1) ◽  
pp. 103-119
Author(s):  
Genji Yamazaki
Keyword(s):  
Exponential Distribution ◽  
Stationary Distribution ◽  
Queueing System ◽  
Random Selection ◽  
Setup Times ◽  
Product Form ◽  
Service Discipline ◽  
Stationary Distributions ◽  
Server Queue

We consider a K-node queueing system sharing a setup server. Each node has a node server, a waiting position, and a service position, and it behaves as an M/G/1/2 type queue except that each job in the waiting position requires a setup by the setup server to move to the service position. The service discipline of the setup server is nonpreemptive work-conserving random selection. The setup times have a common exponential distribution. The main purpose of this paper is to derive the stationary distribution for the K-node system. For each node, we construct a corresponding setup server queue (CSQ). The stationary distribution of the K-node system is given by a product form of the stationary distributions of CSQs. This result enables us to obtain the stationary distribution of a K-node system by analyzing individual CSQs.

Analysis of Queueing System with Non-Preemptive Time Limited Service and Impatient Customers

2019 ◽  
Vol 22 (2) ◽  
pp. 401-432
Author(s):  
Chesoong Kim ◽  
Alexander Dudin ◽  
Olga Dudina ◽  
Valentina Klimenok
Keyword(s):  
Queueing System ◽  
Impatient Customers ◽  
Limited Service

Analysis of a discrete-time queueing system with time-limited service

1994 ◽  
Vol 18 (1-2) ◽  
pp. 183-197 ◽  
Author(s):  
Hideaki Takagi ◽  
Kin K. Leung
Keyword(s):  
Discrete Time ◽  
Queueing System ◽  
Limited Service

scholarly journals A single-server queue with random accumulation level

1991 ◽  
Vol 4 (3) ◽  
pp. 203-210 ◽  
Author(s):  
Jewgeni H. Dshalalow
Keyword(s):  
Continuous Time ◽  
Queueing System ◽  
Time Parameter ◽  
Single Server ◽  
Single Server Queue ◽  
Explicit Formulas ◽  
Stationary Distributions ◽  
Random Size ◽  
Queueing Process ◽  
Server Queue

The author studies the queueing process in a single-server bulk queueing system. Upon completion of a previous service, the server can take a group of random size from customers that are available. Or, the server can wait until the queue attains a desired level. The author establishes an ergodicity criterion for both the queueing process with continuous time parameter and the imbedded process. Under this criterion, the author obtains explicit formulas for the stationary distributions of both processes by using semi-regenerative techniques.

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