Modelling Dynamic Traffic Loads in Multiserver Queues using G/G/k Queue

Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Tamilnadu -603203.

Abstract

Operations research and marketing management have benefited greatly from the important science of queuing optimisation. We take into account a multiserver single input G/G/k queue for study. This type of queue formation occurs in factories, production facilities, logistics centres, airports, and hospitals where the inter-arrival and service times are frequently not exponentially distributed. Knowing the precise number of service providers needed to avoid congestion at the lowest possible cost would therefore be the main concern. When there are more jobs than servers in a G/G/k queue, the cost incurred by the number of jobs per unit time becomes complex, making it challenging to determine the average cost. As a result, this paper obtains the bound for the ideal number of servers that would reduce the overall cost. Interpolation technique is used to determine the precise number of servers. When there are more servers (k) than job arrivals, the G/G/k queue’s optimal cost per unit time during an execution cycle is obtained. The proposed system is made up of a G/G/k queue that begins operating as soon as the first job enters the system. Due to the general distribution of job arrivals, the time interval between subsequent job arrivals is not always the same. Therefore, the study of an arrival that causes a state transition in the system is taken into account. When there are fewer servers available than job arrivals, an expression is derived to determine the optimal server count. When the number of available servers exceeds the number of jobs in the system, the optimal number of jobs that minimises the average processing cost per unit time for one job is also determined. The simulation results are obtained by simulating this system with MATLAB’s SimEvents toolbox.