Analysis of the Discrete-Time G(G)/Geom/c Queueing Model

Abstract

Abstract. This paper presents the steady-state analysis of a discretetime infinite-capacity multiserver queue with c servers and independent geometrically distributed service times. The arrival process is a batch renewal process, characterized by general independent batch interarrival times and general independent batch sizes. The analysis has been carried out by means of an analytical technique based on generating functions, complex analysis and contour integration. Expressions for the generating functions of the system contents during an arrival slot as well as during an arbitrary slot have been obtained. Also, the delay in case of a firstcome-first-served queueing discipline has been analyzed.

Performance analysis of a GI[X]/Geo/m/NGoswami1, Samanta2 2007Computers & Mathematics with Applications2000View full textAdd to dashboardCite

“…The Geo X /Geo/m queue with batch arrivals has been analyzed by Rubin and Zhang [9]. Wittevrongel et al [10] have carried out an analysis of the discrete-time G (G) /Geo/m queueing model. The discretetime multiserver queueing models with constant, equal to one slot or multiple slots, service times is analyzed by Chaudhry and Kim [11], and Bruneel and Wuyts [12] wherein they have discussed the shared-memory architecture which has multiple output channels as an application of the discrete-time multiserver queues.…”

Analytically Simple and Computationally Efficient Results for the GIX/Geo/c Queues

“…Besides, none of the above authors consider heavy-tailed inter-arrival times. Similarly, Wittevrongel et al [30] solve using complex analysis and contour integration while only considering the EAS with no numerical results. Lastly, Chaudhry et al [31] solve using the supplementary variable technique that consider the light-tailed inter-batcharrival times only.…”

Analyzing discrete-time bulk-serviceGeo/Geob/mqueue

“…Further, Chaudhry et al [9] have discussed a more complex model: GI X /Geo/m. In this connection see also papers by Chaudhry and Kim [8], Wittevrongel et al [19]. The transient behaviour of the Geo/Geo/m/m queue (discrete version of Erlang loss model) has been studied by Chaudhry and Gupta [5].…”