Stationary Analysis of the M/M/1 Queuing System with Two Customer Subgroups

Abstract A single server Markovian queuing system called the M/M/1 queuing system with two distinct customer types namely; the constraint customer type and the un-constraint customer type is studied. This model is that of a production system with heterogeneous customer structures devoid of a single customer in the intersection category group wise. Initially, relevant literature covering methodologies, analysis and results derived for single server production systems are reviewed and a gap identified. The gap is that: The application of group theory in the analysis of queuing systems is scarce in the literature. This is against the backdrop that most customers of service systems of transportation, telecommunications, computer systems and other production centers exhibit certain group characteristics. This gap motivated us to impose a group structure on customers of the queuing system in question with the property that for the two subgroups considered in this work, their intersection is null. Using the generating function approach, we provided results on the stationary impact of one subgroup on the other. These results are fundamental basis for optimizing performance of sectors and sub-sectors of production centers relative to their distributions and expectations generally.