Suppose you’re designing a toll bridge for vehicle traffic over the Cache la Poudre River. Cars are expected to arrive at the central toll plaza at a rate of 400 per hour. You will have five toll booths, which can each process cars at a rate of 120 cars per hour. Assume cars arrive into the toll plaza according to a Poisson distribution with a mean rate of 400 units per period. Assume car processing times are exponentially distributed with a mean service rate of 120 units per period. 1. What is the probability that two channels are busy and no units are waiting in the queue? 2. What is the steady-state average length of the queue (waiting line)? 3. What is the mean number of units in the system (queue and service)?
Suppose you’re designing a toll bridge for vehicle traffic over the Cache la Poudre River. Cars are expected to arrive at the central toll plaza at a rate of 400 per hour. You will have five toll booths, which can each process cars at a rate of 120 cars per hour. Assume cars arrive into the toll plaza according to a Poisson distribution with a mean rate of 400 units per period. Assume car processing times are exponentially distributed with a mean service rate of 120 units per period.
1. What is the probability that two channels are busy and no units are waiting in the queue?
2. What is the steady-state average length of the queue (waiting line)?
3. What is the mean number of units in the system (queue and service)?
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