Problems Queuing Models
 Problems for Queuing Models - Fill in the Blanks 3

The flow in a downtown restaurant is measured in parties, where a party is a group of people that will use a single table. The restaurant has ten tables and waiting space for five parties. On a rainy evening, the arrival rate to the restaurant is 10 parties per hour. Once seated, the average time for a party to complete the ordering and eating process is one hour. The time between arrivals has an exponential distribution. Although the service process is not exponential we make the Poisson assumption for analysis purposes. When an arriving party finds the waiting spaces full, it does not stay. Rather it rushes off to a neighboring fast food restaurant that has no limit to service. Part of the analysis for this system appears below. Fill in the empty cells. Times are in hours.

 Quantity Value Units Type Mean Number in Queue 1.55 parties Mean Time in Queue hours Mean Number in Service parts Mean Time in Service 1 hour Throughput Rate parts/hour Prob. all servers are busy 0.621 Prob. System Full 0.104

If the restaurant adds another waiting space (to make 6 in all), how will the “Prob. All Servers Busy” change? (up, down, or stay the same) Justify your conclusion.

Operations Research Models and Methods
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by Paul A. Jensen