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**Analysis of a discrete-time queue with load dependent service under discrete-time Markovian arrival process.**
*(English)*
Zbl 1304.60105

Summary: In the study of normal queueing systems, the server’s average service times are generally assumed to be constant. However, in numerous applications this assumption may not be valid. To prevent congestion in overload control telecommunication networks, the transmission rates vary depending on the number of packets waiting in the queue. As traffics in telecommunication networks are of bursty nature and correlated, we assume that arrivals follow the discrete-time Markovian arrival process. This paper analyzes a queueing model in which the server changes its service times (rates) only at the beginning of service depending on the number of customers waiting in the queue. We obtain the steady-state probabilities at various epochs and some performance measures. In addition, varieties of numerical results are discussed to display the effect of the system parameters on the performance measures.

### MSC:

60K25 | Queueing theory (aspects of probability theory) |

90B22 | Queues and service in operations research |

### Keywords:

discrete-time Markovian arrival process; imbedded Markov chain; queue length dependent service; steady-state probability; supplementary variable technique
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\textit{U. C. Gupta} et al., J. Korean Stat. Soc. 43, No. 4, 545--557 (2014; Zbl 1304.60105)

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