scholarly journals Phase-Type Arrivals and Impatient Customers in Multiserver Queue with Multiple Working Vacations

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Cosmika Goswami ◽  
N. Selvaraju
Keyword(s):  
Blocking Probability ◽  
Death Process ◽  
Impatient Customers ◽  
Working Vacation ◽  
Multiple Working Vacations ◽  
Phase Type ◽  
Working Vacations ◽  
The One ◽  
Vacation Period ◽  
Stationary Probability Vector

We consider a PH/M/c queue with multiple working vacations where the customers waiting in queue for service are impatient. The working vacation policy is the one in which the servers serve at a lower rate during the vacation period rather than completely ceasing the service. Customer’s impatience is due to its arrival during the period where all the servers are in working vacations and the arriving customer has to join the queue. We formulate the system as a nonhomogeneous quasi-birth-death process and use finite truncation method to find the stationary probability vector. Various performance measures like the average number of busy servers in the system during a vacation as well as during a nonvacation period, server availability, blocking probability, and average number of lost customers are given. Numerical examples are provided to illustrate the effects of various parameters and interarrival distributions on system performance.

scholarly journals An M/G/1 Retrial Queueing System with Phase Type Services and Working Vacations

2018 ◽  
Vol 7 (4.10) ◽  
pp. 758
Author(s):  
P. Rajadurai ◽  
R. Santhoshi ◽  
G. Pavithra ◽  
S. Usharani ◽  
S. B. Shylaja
Keyword(s):  
Queueing System ◽  
Retrial Queue ◽  
Probability Generating Function ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Multiple Working Vacations ◽  
Phase Type ◽  
Working Vacations ◽  
Multi Phase ◽  
Number Of Customers

A multi phase retrial queue with optional re-service and multiple working vacations is considered. The Probability Generating Function (PGF) of number of customers in the system is obtained by supplementary variable technique. Various system performance measures are discussed. 

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 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 The Discrete-Time Bulk-ServiceGeo/Geo/1Queue with Multiple Working Vacations

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Jiang Cheng ◽  
Yinghui Tang ◽  
Miaomiao Yu
Keyword(s):  
Discrete Time ◽  
Queue Length ◽  
Busy Period ◽  
Operator Method ◽  
Embedded Markov Chain ◽  
Working Vacation ◽  
Early Arrival ◽  
Multiple Working Vacations ◽  
Bulk Service ◽  
Working Vacations

This paper deals with a discrete-time bulk-serviceGeo/Geo/1queueing system with infinite buffer space and multiple working vacations. Considering an early arrival system, as soon as the server empties the system in a regular busy period, he leaves the system and takes a working vacation for a random duration at timen. The service times both in a working vacation and in a busy period and the vacation times are assumed to be geometrically distributed. By using embedded Markov chain approach and difference operator method, queue length of the whole system at random slots and the waiting time for an arriving customer are obtained. The queue length distributions of the outside observer’s observation epoch are investigated. Numerical experiment is performed to validate the analytical results.

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