Q$6.$

a$)$ A self$-$service stores employee's one cashier at its corner. Nine customers arrive on an

average every $5$ minutes while cashier can serve $10$ customers in $5$ minutes. Assuming

Poisson distribution for arrival rate and exponential distribution for service rate,

Find

i$)$ Average number of customers in the system

ii$)$ Average time a customer spends in the system

iii$)$ Average queue length.

$(8$ marks$)$

b$)$ The arrivals at an ATM booth are assumed to be exponentially distributed. The arrival $4$

per hour and the service rate is $12$ per hour.

Determine:

i$)$ Average number of customers in the system

ii$)$ Average number of customer waiting to be served or average queue length

iii$)$ Average time a customer spends system

iv$)$ Average waiting time of a customer before being served. $(12$ marks$)$