A restaurant at a popular Colorado casino provides priority service to player's card holders. The restaurant has 10 tables or booths where customers may be seated. The service time (time a booth or table is occupied) averages 40 minutes once a party is seated. The customer arrival rate is 12 parties per hour, with the parties being equally divided between card holders and people without player's cards. What is the average time that parties without player's cards wait to be seated?

Question

Quizplus · Accepted Answer

The restaurant operates as an M/M/10 queue system. With a service rate of 1.5 parties per hour per table (60/40), the system is at full capacity with 12 parties arriving per hour. Non-card holders wait longer due to priority given to card holders, resulting in an average wait time of approximately 12 minutes.

A Restaurant at a Popular Colorado Casino Provides Priority Service