helpQUESTION $5[20$ MARKS$]$

The guest service supervisor at a hotel in Teluk Cempedak wants to examine the performance

of its reception counters. An average of $96$ guests per day arrive at the hotel and queue in a

single line such that the queue discipline is first come, first serve $($FCFS$).$ The hotel receptionist

operates for $12$ hours per day, and the average time taken for a receptionist to serve a customer

is $12$ minutes. Suppose that the arrival and service time distribution are both exponentials.

$($a$)$ Find the average number of guests that will be serviced by a receptionist in one hour.

$[2$ Marks$]$

$[$CO$1,$ PO$1,$ C$3]$

$($b$)$ The supervisor wants to assign only one receptionist during weekdays. On Monday,

determine, the

i$)$ average number of customers at the reception counter per hour.

$[2$ Marks$]$

$CO2,PO2,C3$

ii$)$ average number of guests waiting in the queue per hour.

$[2$ Marks$]$

$CO2,PO2,C3$

iii$)$ average time spent $($in minutes$)$ at the reception counter per guest.

iv$)$ average waiting time in the queue $($in minutes$)$ per guest.

v$)$ probability of a receptionist to be idle.

$($c$)$ To improve the reception counter performance, the supervisor attempts to assign two

receptionists during weekends. Find, the new

i$)$ average number of guests waiting in the queue per hour.

ii$)$ average waiting time in the queue $($in minutest$)$ per guest.