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Please help me figure out
Average service time:
Arrival rate:
Lambda :
Mu:

THE CURRENT PLAN OF THE HOTEL
Ellen Elkin, manager of the Hawaiian Village Beach Resort, a resort hotel on Waikiki Beach in Honolulu, Hawaii has requested your assistance on a queuing issue to improve the guest service at the hotel lobby. Ellen Elkin is considering how to restructure the front desk to reach an optimal level of staff efficiency and guest service. Observation of arrivals during the peak check-in time of 5:00PM to 7:00PM shows that an average of 50 guests arrive each hour. It takes an average of 5 minutes for the front-desk clerk to register each guest. Ms. Elkin is considering plans for improving guest service by reducing the length of time that guests spend waiting in line.

PLAN II. Plan 2 would designate one employee as a quick-service clerk for guests registering under corporate accounts, a market segment that fills about 30% of all occupied rooms. Because corporate guests are pre-registered, the registration takes an average of just 3 minutes. With these guests separated from the rest of the clientele, the average time for registering a typical guest would climb to 6 minutes. Under this plan non-corporate guests would choose any of the remaining four lines.

Determine the average amount of time that a guest spends checking-in under each of the stated options and compare to existing set-up. HINT: for Plans with multiple “systems” (eg. 30% corporate customers, 70% regular customers) calculate a weighted average time for that plan so you can easily compare performance measures to the other plans.

Below is the hotels current plan if you need it!

PLAN I. (CURRENT PLAN): At present, the hotel has five clerks on duty, each with a separate waiting line.