The customer arrival process for a given service is of Poisson Distribution

Queueing Theory

The customer arrival process for a given service is of Poisson Distribution with average arrival rate being every 10 minutes. The duration of a service can be considered as a Negative Exponential distribution with average value equal to 8 minutes. Knowing that the system works with a single server and cannot receive more than 5 clients, determine:

a)

i) The type of queue system associated with the problem stated, justifying the characterization in detail.

ii) The average number of customers per hour prevented from entering

iii) The average length of the queue

iv) The average permanency time of a customer in the system and in the queue.

b) Assuming that the system works with 2 servers, which is the average number of customers per hour barred from entering and what is the average queue length?