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

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 III. Plan 3 is to implement a single-line system. All guests could form a single waiting line to be served by whichever of five clerks became available. (The only difference between Plan I (the current scenario) and this proposed Plan III is the line formation currently it is set up with five separate lines one in front of each of the clerks, this plan III proposes a single line that wraps around with a corral and the next guest will go to the next available clerk). This option would require sufficient lobby space for what could be a substantial queue.

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.