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 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.

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.

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.

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 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.

The analysis of a discrete time finite-buffer queue with working vacations under Markovian arrival process and PH-service time

2020 ◽  
Vol 54 (3) ◽  
pp. 675-691
Author(s):  
Qingqing Ye ◽  
Liwei Liu ◽  
Tao Jiang ◽  
Baoxian Chang
Keyword(s):  
Performance Measures ◽  
Discrete Time ◽  
Loss Probability ◽  
Combination Method ◽  
Arrival Process ◽  
Finite Buffer ◽  
The Matrix ◽  
Working Vacations ◽  
The Impact ◽  
Number Of Customers

In this paper, we study the discrete-time MAP/PH/1 queue with multiple working vacations and finite buffer N. Using the Matrix-Geometric Combination method, we obtain the stationary probability vectors of this model, which can be expressed as a linear combination of two matrix-geometric vectors. Furthermore, we obtain some performance measures including the loss probability and give the limit of loss probability as finite buffer N goes to infinite. Waiting time distribution is derived by using the absorbing Markov chain. Moreover, we obtain the number of customers served in the busy period. At last, some numerical examples are presented to verify the results we obtained and show the impact of parameter N on performance measures.

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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