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
\(L_{q}=\frac{\rho^{2}}{2(1-\rho)}\)
iii. Average waiting time in the system
\(W_{s}=\frac{(2-p)}{2 \mu(1-p)}\)
iv. Average waiting time in the queue
\(\mathrm{W}_{q}=\frac{\rho}{2 \mu(1-\rho)}\)