All trucks traveling on a major highway must stop at a weigh station. Trucks arrive at a rate of 200 per 8-hour day. The station can currently weigh on average 220 trucks per 8-hour day. Assume that the arrival rate follows a Poisson distribution and the service time is exponentially distributed. Based on the queuing formulas, the trucks are spending on average 24 minutes at the weigh station and there are on average 10 trucks at the weigh station. The state believes that this is too much time spent at the weigh station and as a result truck drivers are taking a different route or driving at night after the weigh station is closed. As a result, the state estimates that it cost them $10 in taxes, fees and fines for each minute a truck driver has to spend at the weigh station. The state is considering outsourcing the activity at the weigh station and has received two proposals:
? The first company will increase the number of trucks on average that are weighed to 240 trucks per 8-hour day. This will reduce the average time a truck spends at the weigh station to 12 minutes and there would be on average 5 trucks at the weigh station. This company will charge $15,000 per day to run the weigh station.
? The second company will increase the number of trucks on average that are weighed to 230 trucks per 8-hour day. This will reduce the average time a truck spends at the weigh station to 16 minutes and on average 6.67 trucks at the weigh station. This company will charge $10,000 per day to run the weigh station.
Under either proposal, the state will continue to maintain and upkeep the weigh station and all of the equipment there.
Should the state continue to operate the weigh station itself or should it outsource it to one of the two companies? If it should outsource it, which company should the state select. Show your work and base your decision on the economics of the operation.
This posting contains solution to following queuing analysis problem involving cost analysis.