Problem # 1
Parts arrive for packaging at a Poisson rate of 30/hour. The time required for packaging is normally distributed with a mean of 3 minutes and a standard deviation of 1 minute. If the system operates as an Erlang loss system, how many stations should be provided in order to have no greater than 5% loss?

Problem # 2
An accumulation conveyor is to be provided at a workstation. When the conveyor is full, parts are diverted to another area for processing. Parts arrive at a Poisson rate of 2.0 /minute. The time required to process a part at the workstation is exponentially distributed with a mean of 18 seconds per part. It is desired to provide an accumulation line sufficiently long such that less than 1% of the arriving parts will be diverted to another area of processing. What is the minimum number of waiting spaces that will satisfy the objective?

Problem # 3
Consider a distribution center that uses a fleet of six battery-powered automated guided vehicles for material delivery. Due to the wide variety of demands placed on the AGV, the life of a battery, before recharging is required, is a random variable. Suppose the time from recharging a battery for an AGV until it requires recharging again is exponentially distributed with a mean value of 10 hours. Also, suppose the AGV is idle during battery recharging. Finally, suppose the time required to recharge a battery is also exponentially distributed with mean of 2 hours. There are two battery-recharging stations, and the distribution center operated 24 hours/ day and seven days per week.
a) Determine the probability of at least one battery recharging station being idle.
b) Determine the average number of AGVs waiting to be recharged.

Problem # 4
Discuss the different assumptions of open and closed queuing network models. Confronted with a real system, what factors would determine which modeling approach to use?

Problem # 6
A job shop has three types of machines; two mills, one drill press, and one surface grinder. Orders arrive to the shop at a rate of 2 per day. About 60% of these go to milling first. The other 40% start at the drill. One half of the drilling jobs go next to milling, whereas the other one half leave the system. Thirty percent of jobs being milled are sent for grinding, and the others leave the shop.
Jobs always leave the system after grinding. Operation times are exponentially distributed, averaging one day per job for milling, drilling, and grinding. Find the average number of jobs in the system.

Problem # 1 Parts arrive for packaging at a Poisson rate of 30/hou...