Concierge Consider the concierge service at a large resort. The concierge helps

Question

Concierge Consider the concierge service at a large resort. The concierge helps guest with various tasks, including reservations at local restaurants or offering advice on various local activities. On average 12 guests arrive at the concierge desk per hour (the standard deviation of the inter arrival times is equal to 5 minutes). The hotel has only one concierge on service. It takes the concierge, on average 4 minutes to help the guest with their questions. The standard deviation of tis time is three minutes.

C1. What is the average time a guest has to wait before talking to the concierge?

C2. How many guests will on average, be at the concierge’s desk (either talking to the concierge or waiting in line)?

Explanation / Answer

C1. Here the average waiting time has to be identified.

The formula for the waiting time for one resource can be utilized here.

Given,

The activity time = 4 minutes.

Flow rate = 12 guests per hour

The utilization can be calculated as below

U= flow rate/ capacity

=12/15

= 0.8

In order to identify the average waiting time CVa and CVp has to be identified.

CVa = std dev (inter-­-arrival times) / avg(inter-­-arrival times) = 1

CVp = std dev(processing times) / avg(processing times) = 0.75

Now average waiting time can be identified

Average waiting time = activity time × (utilization/ CVa- utilization)×(CVa2+CPa2/2)

=4×0.8 / (1-0.8)) × ((12 + 0.752)/2) = 12.5 minutes

C2

Here little’s law can be utilized

Inventory = flow rate× flow time

Flow rate = 12 guests per hour

Flow time = waiting time + processing time

= 12.5 min + 4 min

= 16.5 min

which can be converted to hour = 0.275 hr

Hence the average number of guests on desk

= 12 ×0.275

= 3.3 guests

which can be rounded as 3

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