Transient analysis of M/M/C queuing model with reneging, finite capacity and population

Abstract

The present paper deals with multi-server Markovian queuing model with impatient behaviour of units. The server work in two modes: slow mode and fast mode; and changes its state from slow to fast or vice versa with some exponential distributed time parameters. When the server works in slow mode, the units may leave the system due to impatient behaviour of units. We investigate the present model by two variant, one with finite capacity and other with finite population. Transient probabilities of various states are obtained by solving the set of governing equation via Runge-Kutta method. The various system performance measures are established in terms of transient probability of the system states. The system behaviour for different parameter are analysed by using the graphs and tables.

Traffic Flow Optimization: Modeling the Inter-Arrival Times for Simulation Model

“…There are many types of modern optimization approaches, but simulation is widely used and seems reliable to cater traffic management problem. Generally, in the traffic engineering and queuing analysis field, the randomness of vehicle time between arrivals is considered exponentially distributed (Adam, 1950;El-Hadidy et al, 2021;Jose, 2021;Kumar, 2022;Meng et al, 2009;Saritha et al, 2022;Sumaryo et al, 2015;Wang et al, 2021). Sumaryo et al (2015) used queuing models M/M/1 and M/G/1 to model traffic flow circumstances.…”

“…Researchers in discrete-event simulation modelling, on the other hand, tend to use the distributions for inter-arrival and process times recommended by the built-in tools (Frough et al, 2019;El-Hadidy et al, 2021;Jose, 2021;Kumar, 2022;Meng et al, 2009;Saritha et al, 2022;Sumaryo et al, 2015;Wang et al, 2021). Arena Input Analyzer, for example, one of the most widely used tools, provides the best distribution based on the smallest mean square error value.…”