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M/PH/1 QUEUE WITH DETERMINISTIC IMPATIENCE TIME

Kim, Jerim;Kim, Jeongsim

  • Received : 2011.08.08
  • Published : 2013.04.30

Abstract

We consider an M/PH/1 queue with deterministic impatience time. An exact analytical expression for the stationary distribution of the workload is derived. By modifying the workload process and using Markovian structure of the phase-type distribution for service times, we are able to construct a new Markov process. The stationary distribution of the new Markov process allows us to find the stationary distribution of the workload. By using the stationary distribution of the workload, we obtain performance measures such as the loss probability, the waiting time distribution and the queue size distribution.

Keywords

M/PH/1 queue;impatience time;workload;loss probability;waiting time distribution;queue size distribution

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Cited by

  1. MAP/M/c and M/PH/c queues with constant impatience times vol.82, pp.3-4, 2016, https://doi.org/10.1007/s11134-015-9455-9
  2. Discrete-time renewal input queue with balking and multiple working vacations vol.10, pp.3, 2015, https://doi.org/10.1080/17509653.2014.954651
  3. Analysis of the loss probability in the M/G/1+G queue vol.80, pp.4, 2015, https://doi.org/10.1007/s11134-015-9449-7
  4. Multi-class M/PH/1 queues with deterministic impatience times vol.33, pp.1, 2017, https://doi.org/10.1080/15326349.2016.1197778

Acknowledgement

Supported by : Chungbuk National University