Development of A Generalised Solution for The Performance Measures of Queuing Systems

ABSTRACT

This study developed computer software with the capacity to provide a generalized solution to queuing problems involving laborious, time consuming and complex mathematical approach of evaluating the performance measures of queuing systems when it was applied in the analysis of the six (6) fundamental performance measures of thirty (30) different organizations representing the six (6) queuing systems; the result was compared with that of mathematical computations and 97.22% compliance was observed from the 180 computations made with 2.78% discrepancy. It was also observed that the number of servers required to attain steady state for the waiting cost is linearly proportional to the arrival rate (λ) and inversely proportional to the service rate (µ). It also he effect of λ and µ on the cost variable profiles depend on the magnitude of both parameters such that: when λ = μ, Identical cost variables profiles is observed, when λ > µ, Unpredictable random fluctuations and when λ < µ, Defined fluctuations of cost variables profiles is observed. In addition, the cost variables profiles experience discontinuities at number of servers less than 2 but experience continuities at number of servers from 2 upwards. Therefore, the software can analyze finite and infinite queuing systems; single and multi-server queuing systems; all the six queuing systems; all the fundamental performance measures; many derived performance measures and with the added advantage of cost evaluations. It is therefore recommended to both individuals and organisations with businesses involving the analysis of queuing systems.