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
4.4. M/M/c/k Queue
In this model, customers arrive according to a Poisson process describing independent and exponentially distributed inter-arrival times. The service times are also assumed to be independent and exponentially distributed. The difference of this model with the previous models is the only k customers who can get the service by fixed number of c servers. Followings are the formulae for some of the performance measures of this queueing system.
ii. Probability of having customers in the syste
iii. Average number of customers in the system
iv. Average number of customers in queue
v. Average waiting time in the system
vi. Average waiting time in the queue