• Title, Summary, Keyword: PH-retrial time

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ON APPROXIMATIONS FOR GI/G/c RETRIAL QUEUES

  • Shin, Yang Woo;Moon, Dug Hee
    • Journal of applied mathematics & informatics
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    • v.31 no.1_2
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    • pp.311-325
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    • 2013
  • The effects of the moments of the interarrival time and service time on the system performance measures such as blocking probability, mean and standard deviation of the number of customers in service facility and orbit are numerically investigated. The results reveal the performance measures are more sensitive with respect to the interarrival time than the service time. Approximation for $GI/G/c$ retrial queues using $PH/PH/c$ retrial queue is presented.

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
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    • v.19 no.1
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    • pp.169-175
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    • 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.

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

  • Shin, Yang-Woo
    • Journal of applied mathematics & informatics
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    • v.29 no.3_4
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    • pp.803-811
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    • 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.

STABILITY OF MAP/PH/c/K QUEUE WITH CUSTOMER RETRIALS AND SERVER VACATIONS

  • Shin, Yang Woo
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.4
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    • pp.985-1004
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    • 2016
  • We consider the MAP/PH/c/K queue in which blocked customers retry to get service and servers may take vacations. The time interval between retrials and vacation times are of phase type (PH) distributions. Using the method of mean drift, a sufficient condition of ergodicity is provided. A condition for the system to be unstable is also given by the stochastic comparison method.