Question

With the capital city and the surrounding areas becoming increasingly dangerous in the nights, a budding entrepreneur started a venture called "Walk-with-a-Friend" service. The system consists of specially trained friendly security personnel that accompany elderly people, working women or anyone else who has to access the nearest auto stand, bus stand or other amenities in late in the night. The service is operated 24 hours a day, seven days a week. Owing to its instant success, residents in Noida have been requesting for "Friends", on average, every 5 minutes randomly. After receiving the request on the app, a central agency contacts and available and nearby "Friend", who immediately proceeds to pick up the client and walk him/her to their destination (and have a friendly chat on the way). If there are no "Friends" available at that time, the central agency puts the request in queue until a friend becomes available. A Friend takes, on average, 15 minutes for meeting the client and dropping them to their destination. Currently, the sector in which they are operating has only 6 friends. The requests for friends and the service rate have a coefficient of variation of 1 and 1.5 respectively.

a) How many friends are, on average, available to satisfy a new request?

b) How much time does it take, on average, from the moment a client requests for a friend to the moment the client reaches his/her destination?

c) What is the average number of people waiting in the queue to get their service?

Note to the tutor: Please share the answers with steps

Answer 1

Solution:

Given values,

Hence,

Let's calculate two basic queue parameters first using the above formula.

Hence,

a: How many friends are available for attending requests on an average.

This is equivalent to the utilization of the friends, hence,

Hence, on an average of 50%, that is, 3 friends are available to attend requests.

b: Total time the client spends in the system:

c: Average number of people waiting in the queue to get the service.