Analysis of a Discrete-Time Finite-Capacity Single-Server Queue with Markovian-Arrival Process and Random-Bulk-Service: D-MAP/G^Y/1/M

Abstract

In this article, we consider a single-server, finite-capacity queue with random bulk service rule where customers arrive according to a discrete-time Markovian arrival process (D-MAP). The model is denoted by D-MAP/G ^Y /1/M where server capacity (bulk size for service) is determined by a random variable Y at the starting point of services. A simple analysis of this model is given using the embedded Markov chain technique and the concept of the mean sojourn time of the phase of underlying Markov chain of D-MAP. A complete solution to the distribution of the number of customers in the D-MAP/G ^Y /1/M queue, some computational results, and performance measures such as the average number of customers in the queue and the loss probability are presented.

Keywords:

• Correlated arrival
• Discrete time
• Finite-capacity
• Queueing
• Random-bulk-service

Mathematics Subject Classification:

• 60K25
• 68M20
• 90B18

Notes

Performance Measures: P _loss  = 0.003603, P _busy  = 0.787083, L _q  = 3.056819, Mean batch size of service =2.109895.

*Performance Measures: P _loss  = 0.003292, P _busy  = 0.993972, L _q  = 26.593001, Mean batch size of service =3.705533.

*Performance Measures: P _loss  = 0.003292, P _busy  = 0.993972, L _q  = 26.593001, Mean batch size of service =3.705533.

*Performance Measures: P _loss  = 0.003292, P _busy  = 0.993972, L _q  = 26.593001, Mean batch size of service =3.705533.