Mathematical Models of Mb/M/1 Bulk Arrival Queueing System

Abstract

This paper deals with the study of bulk queueing model with the fixed batch size 'b' and customers arrive to the system with Poisson fashion with the rate λ and are severed exponentially with the rate μ. On formulating the mathematical model, we obtain the expressions for mean waiting time in the queue, mean time spent in the system, mean number of customers/work pieces in the queue and in the system by using generating function method. Some numerical illustrations are also obtained by using MATLAB-7 so as to show the applicability of the model under study.

Performance analysis of SDN vs OSPF in diverse network environments

“…Similar to network delays, the fault location has more impact on OSPF convergence than on SDN convergence speed. In fact, Figure 9 shows that the OSPF convergence delay is smallest when the fault is occurring in the middle of the network (faulty link [23][24][25]. This effect is not observed in Figure 10 for SDN, which is expected because fault location basically affects the time it takes to ripple advertisements throughout the network, and this does occur in SDN.…”

“…The system can be modeled as a M n /M/1 bulk arrival queue, where n is the number of nodes in the network. 24 We assume that rules for a single switch are processed together, and thus, the number of ''customers'' in the queue corresponds to the number of switches. Consequently, the processing time of one ''Flow Mod'' message follows the exponential distribution with parameter , where is the processing rate of the controller.…”

Application of Mb/M/1 Bulk Arrival Queueing System to Evaluate Key-In System in Islamic University of Indonesia

“…Maurya [3] study the bulk arrival retrial queueing MX / G1, G2, / 1 model with two phase service and Bernoulli vacation schedule wherein first phase service is essential and the next second phase service is optional. The objective of this paper is to investigate the steady state behavior of the bulk arrival retrial queueing MX / G1, G2, / 1 model with two phase service and Bernoulli vacation schedule.…”

Service Rate Optimization of Finite Population Queueing Model with State Dependent Arrival and Service Rates

“…D'Auria [5] analysed ∞ queue to study the stochastic decomposition formula for the number of customers in the system with some examples in random environment. Ghimire et al [6] verified formulas for mean queue length and mean waiting time using generating function technique for the batch arrival of customers. Ghimire et al [7] calculated various performance measures for finite capacity time dependent multi-server queueing model and verified the results graphically using simulation.…”