# Case Study Sample About Queues

Topics: Average, Arithmetic mean Pages: 7 (1745 words) Published: January 25, 2013
Background
The manager of the Winter, Donna Shader, is considering how to restructure the front desk to reach an optimum level of staff efficiency and guest service. At the moment, the hotel employs five clerks , each with a separate waiting line, to register the guests during the peak time of 3:00-5:00 PM. Observations show that an average of 90 guests arrive each hour, though there is no upward limit on the number that could arrive at a given time. It takes each desk clerk an average of three minutes to register each guest. Donna is considering designating one employee as a quick-service clerk that would register guests with corporate accounts, a market segment that fills around thirty percent of all occupied rooms. As corporate guests are preregistered, their registration would take only two minutes. This would result in the average time for registering a typical guest to change to 3.4 minutes. Non-corporate would choose any of the remaining four lines. Another option open to management is a single-line system. The guests would form a single waiting line to be served by whichever of the five clerks become available. This would require ample lobby space to accommodate what would be a long line. A third option is to use an automatic teller machine or ATM for check-ins, that would provide approximately the same service rate as would a clerk. Considering that initial use of this technology might be minimal, Shader estimates that twenty percent of the customers, mainly frequent guests, would be willing to use the machines. There would be a single queue for customers who prefer human check-in clerks. This would be served by the five clerks, though Donna is hopeful that the machine would allow a reduction to four.

Statement of the Problem
Which option should Donna Shader employ to lessen the length of time guests spend waiting in line, thereby improving guest service?

Objective
* Reduce the time spent registering each client
* Shorten the waiting line

Alternative Courses of Action
Alternative 1:
Designate one employee as a quick-service clerk for guests registering under corporate accounts. The registration will just take two minutes. With these guests separated from the rest of the clientele, the average time registering a typical guest would climb to 3.4 minutes. Non-corporate guests would choose any of the remaining four lines. Alternative 2:

Implement a single-line system. All guests could form a single waiting line to be served by whichever of five clerks became available. This option would require sufficient lobby for what could be a substantial queue. Alternative 3:

Use an Automatic Teller Machine (ATM) for check-ins. This ATM would provide approximately the same service rate as a clerk would. It is estimated that 20% of customers would be willing to use the machines. A single queue for customers who prefer human check-in clerks. This would be served by the five clerks. Although, Donna is hopeful that the machine will allow a reduction to four.

Present System:

=mean number of arrivals per time period
=mean number of people or items served per time period
=mean number of arrivals per time period
=mean number of people or items served per time period
We let:

= 90 persons per hour = 90/5 = 18 customers per hour
= 3 minutes = 20 per hour
Solution:
9 customers in the system on the average
9 customers in the system on the average
½ hour or 30 minutes that an average customer spends in the system ½ hour or 30 minutes that an average customer spends in the system

0. 45 hour or 27 minutes average waiting time per customer
0. 45 hour or 27 minutes average waiting time per customer
8.1 customers waiting in line on the average
8.1 customers waiting in line on the average
0.9percentage of time clerk is busy
0.9percentage of time clerk is busy
0.1probability that there are 0 customers in the system
0.1probability that there are 0 customers in the...