Quantitative Techniques: Theory and Problems

OPTIMUM VALUE OF SERVICE RATE ()

The study of queuing models helps us to find a cost model which minimises the sum of costs of service and of waiting time per unit time. Generally, it is assumed that the cost of waiting is directly proportional to the total time that the customers spend in the system, both waiting and in service. The service can usually be ascertained from the various available records.

Assuming a single server model with an arrival rate λ and service rate μ and that the service rate μ is controllable, optimum value of service rate μ can be determined as follows:

let

C₁ = cost per unit increase in μ per unit time.

C₂ = cost per ...