• Title, Summary, Keyword: M/M/m retrial queue

Search Result 18, Processing Time 0.032 seconds

Approximation of M/G/c Retrial Queue with M/PH/c Retrial Queue

  • Shin, Yang-Woo;Moon, Dug-Hee
    • Communications for Statistical Applications and Methods
    • /
    • v.19 no.1
    • /
    • pp.169-175
    • /
    • 2012
  • The sensitivity of the performance measures such as the mean and the standard deviation of the queue length and the blocking probability with respect to the moments of the service time are numerically investigated. The service time distribution is fitted with phase type(PH) distribution by matching the first three moments of service time and the M/G/c retrial queue is approximated by the M/PH/c retrial queue. Approximations are compared with the simulation results.

TAIL ASYMPTOTICS FOR THE QUEUE SIZE DISTRIBUTION IN AN MX/G/1 RETRIAL QUEUE

  • KIM, JEONGSIM
    • Journal of applied mathematics & informatics
    • /
    • v.33 no.3_4
    • /
    • pp.343-350
    • /
    • 2015
  • We consider an MX/G/1 retrial queue, where the batch size and service time distributions have finite exponential moments. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. Our result generalizes the result of Kim et al. (2007) to the MX/G/1 retrial queue.

AN APPROXIMATION FOR THE QUEUE LENGTH DISTRIBUTION IN A MULTI-SERVER RETRIAL QUEUE

  • Kim, Jeongsim
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.29 no.1
    • /
    • pp.95-102
    • /
    • 2016
  • Multi-server queueing systems with retrials are widely used to model problems in a call center. We present an explicit formula for an approximation of the queue length distribution in a multi-server retrial queue, by using the Lerch transcendent. Accuracy of our approximation is shown in the numerical examples.

ALGORITHMIC SOLUTION FOR M/M/c RETRIAL QUEUE WITH $PH_2$-RETRIAL TIMES

  • Shin, Yang-Woo
    • Journal of applied mathematics & informatics
    • /
    • v.29 no.3_4
    • /
    • pp.803-811
    • /
    • 2011
  • We present an algorithmic solution for the stationary distribution of the M/M/c retrial queue in which the retrial times of each customer in orbit are of phase type distribution of order 2. The system is modeled by the level dependent quasi-birth-and-death (LDQBD) process.

THE M/G/1 FEEDBACK RETRIAL QUEUE WITH BERNOULLI SCHEDULE

  • Lee, Yong-Wan;Jang, Young-Ho
    • Journal of applied mathematics & informatics
    • /
    • v.27 no.1_2
    • /
    • pp.259-266
    • /
    • 2009
  • We consider an M/G/1 feedback retrial queue with Bernoulli schedule in which after being served each customer either joins the retrial group again or departs the system permanently. Using the supplementary variable method, we obtain the joint generating function of the numbers of customers in two groups.

  • PDF

WAITING TIME DISTRIBUTION IN THE M/M/M RETRIAL QUEUE

  • Kim, Jeongsim;Kim, Jerim
    • Bulletin of the Korean Mathematical Society
    • /
    • v.50 no.5
    • /
    • pp.1659-1671
    • /
    • 2013
  • In this paper, we are concerned with the analysis of the waiting time distribution in the M/M/m retrial queue. We give expressions for the Laplace-Stieltjes transform (LST) of the waiting time distribution and then provide a numerical algorithm for calculating the LST of the waiting time distribution. Numerical inversion of the LSTs is used to calculate the waiting time distribution. Numerical results are presented to illustrate our results.

INTERPOLATION APPROXIMATION OF $M/G/c/K$ RETRIAL QUEUE WITH ORDINARY QUEUES

  • Shin, Yang-Woo
    • Journal of applied mathematics & informatics
    • /
    • v.30 no.3_4
    • /
    • pp.531-540
    • /
    • 2012
  • An approximation for the number of customers at service facility in $M/G/c/K$ retrial queue is provided with the help of the approximations of ordinary $M/G/c/K$ loss system and ordinary $M/G/c$ queue. The interpolation between two ordinary systems is used for the approximation.

THE ${M_1},{M_/2}/G/l/K$ RETRIAL QUEUEING SYSTEMS WITH PRIORITY

  • Choi, Bong-Dae;Zhu, Dong-Bi
    • Journal of the Korean Mathematical Society
    • /
    • v.35 no.3
    • /
    • pp.691-712
    • /
    • 1998
  • We consider an M$_1$, M$_2$/G/1/ K retrial queueing system with a finite priority queue for type I calls and infinite retrial group for type II calls where blocked type I calls may join the retrial group. These models, for example, can be applied to cellular mobile communication system where handoff calls have higher priority than originating calls. In this paper we apply the supplementary variable method where supplementary variable is the elapsed service time of the call in service. We find the joint generating function of the numbers of calls in the priority queue and the retrial group in closed form and give some performance measures of the system.

  • PDF

APPROXIMATE ANALYSIS OF M/M/c RETRIAL QUEUE WITH SERVER VACATIONS

  • SHIN, YANG WOO;MOON, DUG HEE
    • Journal of the Korean Society for Industrial and Applied Mathematics
    • /
    • v.19 no.4
    • /
    • pp.443-457
    • /
    • 2015
  • We consider the M/M/c/c queues in which the customers blocked to enter the service facility retry after a random amount of time and some of idle servers can leave the vacation. The vacation time and retrial time are assumed to be of phase type distribution. Approximation formulae for the distribution of the number of customers in service facility and the mean number of customers in orbit are presented. We provide an approximation for M/M/c/c queue with general retrial time and general vacation time by approximating the general distribution with phase type distribution. Some numerical results are presented.