An average of 90 patrons per hour arrive at a hotel lobby(interarrival times are exponential), waiting to check in. At present, there are 5 clerks, and patrons are waiting in a singleline for the first available clerk. The average time for a clerkto service a patron is 3 minutes (exponentially distributed).Clerks earn $10 per hour, and the hotel assesses a waitingtime cost of $20 for each hour that a patron waits in line.a Compute the expected cost per hour of the currentsystem.b The hotel is considering replacing one clerk with an Automatic Clerk Machine (ACM). Management esti-mates that 20% of all patrons will use an ACM. An ACM takes an average of 1 minute to service a patron.It costs $48 per day (1 day 8 hours) to operate anACM. Should the hotel install the ACM? Assume thatall customers who are willing to use the ACM wait in asingle queue.
An average of 90 patrons per hour arrive at a hotel lobby
(interarrival times are exponential), waiting to check in. At
present, there are 5 clerks, and patrons are waiting in a single
line for the first available clerk. The average time for a clerk
to service a patron is 3 minutes (exponentially distributed).
Clerks earn $10 per hour, and the hotel assesses a waiting
time cost of $20 for each hour that a patron waits in line.
a Compute the expected cost per hour of the current
system.
b The hotel is considering replacing one clerk with an
Automatic Clerk Machine (ACM). Management esti-
mates that 20% of all patrons will use an ACM. An
ACM takes an average of 1 minute to service a patron.
It costs $48 per day (1 day 8 hours) to operate an
ACM. Should the hotel install the ACM? Assume that
all customers who are willing to use the ACM wait in a
single queue.
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