The truncated queues with bulk arrivals and hyperexponential service time distribution with reneging
This paper deals with the steady-state solution of the queueing system: MX/Hk /1/N with reneging in which (i) units arrive in batches of random size with the interarrival times of batches following negative exponential distribution, (ii) the batches are served in order of their arrival; and (iii) the service time distribution is hyperexponential with k branches. Recurrence relations connecting the various probabilities introduced are found. Some measures of effectiveness are deduced and some special cases are also obtained.
Keywords: queueing system: MX/Hk /1/N, hyperexponential
M.M. Badr. The truncated queues with bulk arrivals and hyperexponential service time distribution with reneging. Acta Scientiae et Intellectus, 1(1), 18-25.
- Gupta, S.K. and Goyal, J.K., "Queues with Poisson input and hyperexponential output with finite waiting space". Oper. Res. 14, 75-81, 1964.
- Gupta, S.K. and Goyal, J.K., "Queues with batch Poisson arrivals and hyperexponential service time distribution". Metrika 10, 171-178, 1966.
- Habib, M.E., “Queues with bulk arrivals and hyperexponential service time distribution”. Tamkang J. Manag. Sci. 7, 31-36, 1986.
- Morse, P.M., "Queues, Inventories and Maintenance". John Wiley, New York, 1958.
- Shawky, A.I. and El - Paoumy, M. S., “The truncated hyperexponential service queues: M/Hk /1/N with balking and reneging”. Far East J. of Theoretical Statistics, 2000.
- J.A. White, J.W. Schmidt and G.K. Bennett, "Analysis of queueing systems". Academic Press, New York, 1975.