A Survey on Queueing Systems with Mathematical Models and Applications

Read this paper on waiting line analysis and queues. It provides a good survey of the theory and uses of this type of analysis. Pay particular attention to sections 1 through 3. How might these models be used to balance firm costs with different levels of customer satisfaction?

4. Formulation of Queueing Models

4.5. M/D/1 Queue

This system represents the single server queue, where arrivals are determined by a Poisson process and service times are deterministic. Some of the performance measures formulae are listed as follows:

i. Average number of customers in the system

L_{s}=\frac{\left(2 \rho-\rho^{2}\right)}{2(1-\rho)}

ii. Average number of customers in queue


iii. Average waiting time in the system

W_{s}=\frac{(2-p)}{2 \mu(1-p)}

iv. Average waiting time in the queue

\mathrm{W}_{q}=\frac{\rho}{2 \mu(1-\rho)}