M/M(a, b)/2/K Controlled Arrival Rates and Interdependent Queueing Model

This study focuses on systems that provide services in batches instead of personalized one-on-one assistance. In order to acquire the probability and features of the queueing system, it first introduces controllable arrival rates and interdependency in the service and arrival processes of such a system. Such models are helpful in various circumstances where arrivals are regulated by non-manual robotic systems. Consider that two parallel servers are homogeneous. The input is assumed to be Poisson (during each epoch of the Poisson occurrence, a single arrival) and controllable according to the speed of arrivals. For assistance, each server is equally likely to take a batch when both servers are accessible. Although there have been studies on bulk service in queuing theory, this novel method aims to provide a link between bulk service and interdependency in the arrival and service processes, as well as controlled arrival rates. M/M(a, b)/2/K is the notation for the system. Steady-state solutions and characteristics of the model are derived and analysed. The outcome of analysis is also numerically shown for various parameter values and levels.