DISCRETE-TIME GIX/GEO/1/N QUEUE WITH WORKING VACATIONS AND VACATION INTERRUPTION

2014 ◽  
Vol 31 (01) ◽  
pp. 1450003 ◽  
Author(s):  
SHAN GAO ◽  
ZAIMING LIU ◽  
QIWEN DU
Keyword(s):  
Discrete Time ◽  
Finite Buffer ◽  
Waiting Time Distribution ◽  
Service Period ◽  
Imbedded Markov Chain ◽  
Working Vacations ◽  
Vacation Interruption ◽  
Service Times ◽  
System Length ◽  
Vacation Period

In this paper, we study a discrete-time finite buffer batch arrival queue with multiple geometric working vacations and vacation interruption: the server serves the customers at the lower rate rather than completely stopping during the vacation period and can come back to the normal working level once there are customers after a service completion during the vacation period, i.e., a vacation interruption happens. The service times during a service period, service times during a vacation period and vacation times are geometrically distributed. The queue is analyzed using the supplementary variable and the imbedded Markov-chain techniques. We obtain steady-state system length distributions at pre-arrival, arbitrary and outside observer's observation epochs. We also present probability generation function (p.g.f.) of actual waiting-time distribution in the system and some performance measures.

Analysis of Finite Buffer Markovian Queue with Balking, Reneging and Working Vacations

2013 ◽  
Vol 4 (1) ◽  
pp. 1-24 ◽  
Author(s):  
P. Vijaya Laxmi ◽  
V. Goswami ◽  
K. Jyothsna
Keyword(s):  
Performance Measures ◽  
Finite Buffer ◽  
State Behavior ◽  
Arrival Times ◽  
Service Period ◽  
Markovian Queue ◽  
Special Cases ◽  
Working Vacations ◽  
Service Times ◽  
Vacation Period

This article presents the analysis of a finite buffer M/M/1 queue with multiple and single working vacations. The arriving customers balk (that is do not join the queue) with a probability and renege (that is leave the queue after joining) according to exponential distribution. The inter-arrival times, service times during a regular service period, service times during a vacation period and vacation times are independent and exponentially distributed random variables. Steady-state behavior of the model is considered and various performance measures, some special cases of the model and cost analysis are discussed.

scholarly journals Finite Buffer GI/M(n)/1 Queue with Bernoulli-Schedule Vacation Interruption under N-Policy

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
P. Vijaya Laxmi ◽  
V. Suchitra
Keyword(s):  
Performance Measures ◽  
Finite Buffer ◽  
Supplementary Variable ◽  
Working Vacation ◽  
Variable Technique ◽  
Special Cases ◽  
Vacation Interruption ◽  
System Length ◽  
Vacation Period ◽  
Bernoulli Schedule

We study a finite buffer N-policy GI/M(n)/1 queue with Bernoulli-schedule vacation interruption. The server works with a slower rate during vacation period. At a service completion epoch during working vacation, if there are at least N customers present in the queue, the server interrupts vacation and otherwise continues the vacation. Using the supplementary variable technique and recursive method, we obtain the steady state system length distributions at prearrival and arbitrary epochs. Some special cases of the model, various performance measures, and cost analysis are discussed. Finally, parameter effect on the performance measures of the model is presented through numerical computations.

scholarly journals Optimization of Balking and Reneging Queue with Vacation Interruption underN-Policy

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
P. Vijaya Laxmi ◽  
V. Goswami ◽  
K. Jyothsna
Keyword(s):  
Performance Measures ◽  
Search Method ◽  
Model Parameters ◽  
Finite Buffer ◽  
Working Vacation ◽  
Swarm Optimization ◽  
Multiple Working Vacations ◽  
Working Vacations ◽  
Vacation Interruption ◽  
System Length

This paper analyzes a finite buffer multiple working vacations queue with balking, reneging, and vacation interruption underN-policy. In the working vacation, a customer is served at a lower rate and at the instants of a service completion; if there are at leastNcustomers in the queue, the vacation is interrupted and the server switches to regular busy period otherwise continues the vacation. Using Markov process and recursive technique, we derive the stationary system length distributions at arbitrary epoch. Various performance measures and some special models of the system are presented. Cost analysis is carried out using particle swarm optimization and quadratic fit search method. Finally, some numerical results showing the effect of model parameters on key performance measures of the system are presented.

scholarly journals A Discrete-Time Queue with Balking, Reneging, and Working Vacations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Veena Goswami
Keyword(s):  
Discrete Time ◽  
Cost Model ◽  
Single Server ◽  
Finite Buffer ◽  
Multiple Working Vacations ◽  
Optimal Service ◽  
Special Cases ◽  
Service Rates ◽  
Working Vacations ◽  
Vacation Period

This paper presents an analysis of balking and reneging in finite-buffer discrete-time single server queue with single and multiple working vacations. An arriving customer may balk with a probability or renege after joining according to a geometric distribution. The server works with different service rates rather than completely stopping the service during a vacation period. The service times during a busy period, vacation period, and vacation times are assumed to be geometrically distributed. We find the explicit expressions for the stationary state probabilities. Various system performance measures and a cost model to determine the optimal service rates are presented. Moreover, some queueing models presented in the literature are derived as special cases of our model. Finally, the influence of various parameters on the performance characteristics is shown numerically.

AN M/G/1 RETRIAL QUEUE WITH GENERAL RETRIAL TIMES, WORKING VACATIONS AND VACATION INTERRUPTION

2014 ◽  
Vol 31 (02) ◽  
pp. 1440006 ◽  
Author(s):  
SHAN GAO ◽  
JINTING WANG ◽  
WEI WAYNE LI
Keyword(s):  
Retrial Queue ◽  
Stochastic Decomposition ◽  
Supplementary Variable ◽  
Waiting Time Distribution ◽  
Working Vacation ◽  
Stationary Probability Distribution ◽  
Working Vacations ◽  
Vacation Interruption ◽  
Vacation Period ◽  
Conditional Stochastic Decomposition

We consider an M/G/1 retrial queue with general retrial times, and introduce working vacations and vacation interruption policy into the retrial queue. During the working vacation period, customers can be served at a lower rate. If there are customers in the system at a service completion instant, the vacation will be interrupted and the server will come back to the normal working level. Using supplementary variable method, we obtain the stationary probability distribution and some performance measures. Furthermore, we carry out the waiting time distribution and prove the conditional stochastic decomposition for the queue length in orbit. Finally, some numerical examples are presented.

scholarly journals Performance Characteristics of Discrete-Time Queue With Variant Working Vacations

2020 ◽  
Vol 11 (2) ◽  
pp. 1-21
Author(s):  
P. Vijaya Laxmi ◽  
Rajesh P.
Keyword(s):  
Discrete Time ◽  
Cost Model ◽  
Probability Generating Function ◽  
System Size ◽  
Service Rate ◽  
Single Server ◽  
Working Vacation ◽  
Optimal Service ◽  
Working Vacations ◽  
Vacation Period

This article analyzes an infinite buffer discrete-time single server queueing system with variant working vacations in which customers arrive according to a geometric process. As soon as the system becomes empty, the server takes working vacations. The server will take a maximum number K of working vacations until either he finds at least on customer in the queue or the server has exhaustively taken all the vacations. The service times during regular busy period, working vacation period and vacation times are assumed to be geometrically distributed. The probability generating function of the steady-state probabilities and the closed form expressions of the system size when the server is in different states have been derived. In addition, some other performance measures, their monotonicity with respect to K and a cost model are presented to determine the optimal service rate during working vacation.

scholarly journals Analysis of Impatient Customers in Queues with Bernoulli Schedule Working Vacations and Vacation Interruption

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Veena Goswami
Keyword(s):  
Performance Measures ◽  
System Size ◽  
Stochastic Decomposition ◽  
Model Parameters ◽  
The Mean ◽  
Working Vacations ◽  
Vacation Interruption ◽  
The Impact ◽  
Vacation Period ◽  
Bernoulli Schedule

This paper analyzes customers’ impatience in Markovian queueing system with multiple working vacations and Bernoulli schedule vacation interruption, where customers’ impatience is due to the servers’ vacation. During the working vacation period, if there are customers in the queue, the vacation can be interrupted at a service completion instant and the server begins a regular busy period with probability 1-q or continues the vacation with probability q. We obtain the probability generating functions of the stationary state probabilities and deduce the explicit expressions of the system sizes when the server is in a normal service period and in a Bernoulli schedule vacation interruption, respectively. Various performance measures such as the mean system size, the proportion of customers served, the rate of abandonment due to impatience, and the mean sojourn time of a customer served are derived. We obtain the stochastic decomposition structures of the queue length and waiting time. Finally, some numerical results to show the impact of model parameters on performance measures of the system are presented.

Sign in / Sign up

Export Citation Format

Share Document