Topic queue system m/m/1 theory The restaurant 20 tables of 6 people. There are
ID: 3047571 • Letter: T
Question
Topic queue system m/m/1 theory
The restaurant 20 tables of 6 people. There are 8 to 9 waitress working at anytime. On a daily basis it serves 400 customers during weekdays and over 1000 customers during weekend. An average of 400 people coming from the restaurant in 3 hours time window of dinner time. It was found out from observation and discussion with manager that each customer spends 55 minutes on average in the restaurant, the queue length is around 36 people on average and the waiting time is around 15 minutes. Find the arrival rate and services rate.
Explanation / Answer
There are 20 tables of 6 people each which means about 120 people can sit in the restaurant. If each customer spends arounf 55 min on average, then, when the first 120 customers arrive, they will leave in the first hour.
Thus in the 3 hour dinner time window a total of 360 customers will come and leave, with a time of 15 min still remaining. The queue length is 36 people and waiting time is 15 min which is also the buffer time equal to 15 min of the 3 hour dinner time remaining.
So the arrival rate thus is approximately 120 people per hour and the service rate = 120 people / 8 waitresses = 15 people per waitress