Question:

(a) Discuss briefly the four basic components of any queueing system.

(b) Explain what you understand by the following models:

(i) (M| M | 1 : N | FCFS)

(ii) (M| M | S : ∞| SIRO)

(iii) (M| Ek | 1 : ∞ | FCFS)

(c) A supermarket has two ladies at the sales counters. Given that the service for each customer is exponential with mean 6 minutes and customers arrive in a Poisson fashion at the counter at the rate of 15 per hour, Determine

(i) the expected percentage of idle time for each lady at the sales counter.

(ii) The probability of having to wait for service.