A Survey on Queueing Systems with Mathematical Models and Applications

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

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