Analysis of queueing system with discrete autoregressive arrivals having DML as marginal distribution


  • Bindu Abraham Mahatma Gandhi University, Kottayam - Kerala
  • Kanichukattu K. Jose St. Thomas College, Mahatma Gandhi University, Kottayam - Kerala



Discrete Autoregressive process of order 1[DAR(1)], Discrete Mittag-Leer distribution (DML), multiserver queue, ATM multiplexer, Matrix analytic methods


In this paper we analyze DAR(1)/D/s Queue with Discrete Mittag-Leffler [DML(α)] as marginal distribution. Simulation study of the sample path of the arrival process is conducted. For this queueing system, the stationary distribution of the system size and the waiting time distribution of an arbitrary packet is obtained with the help of matrix analytic methods and Markov regenerative theory. The quantitative effect of the stationary distribution on system size, waiting time and  the autocorrelation function as well as the parameters of the input traffic is illustrated empirically. The model is applied to a real data on the passenger arrivals at a subway bus terminal in Santiago de Chile and is established that the model well suits this data.


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How to Cite

Abraham, B., & Jose, K. K. (2013). Analysis of queueing system with discrete autoregressive arrivals having DML as marginal distribution. Statistica, 73(3), 317–339.