Consider the following parameters for a queueing system with an infinite queue and infinite calling population....
- Consider the following parameters for a queueing system with an infinite queue and infinite calling population. Arrivals follow the Poisson distribution with an average rate of 12 per hour. Service times are exponentially distributed with an average time of 4 minutes.
Find the set of queue statistics (N, Nq, T, Tq, r), and find the percentage of time that the server is busy.
Homework Answers
Answers in Bold
| Queuing model | ||||
| Serving time= | 4.00 | min | ||
| Lamda = arrival rate = | 12.0 | per hour | ||
| Mu = mean service rate = 60/serving time | 15.0 | per hour | ||
| Serving time= 1/Mu= | 0.067 | hours | ||
| Answer e: | percentage busy, Utilization = rho = lamda / mu = | 0.8000 | 80.0% | |
| Answer a: | Average no. in queue: | |||
| Average no queue =Nq = (rho)2 / (1-rho) | ||||
| Average no of customers waiting in line =Lq = | 3.2000 | customers | ||
| Answer d: | Average time spent in queue: | |||
| Tq = waiting time in the line for service = Nq / lambda = | 0.2667 | hours | ||
| Answer c: | Average time spent in the system: | |||
| T = average time in the system = Tq + serving time = | 0.3333 | hours | ||
| Answer b: | Average no. of customers in system. | |||
| N = no. of customers in the system = T *Lambda = | 4.00 | customers | ||
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Consider the following parameters for a queueing system with an
infinite queue and infinite calling population....
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QUESTION 2:
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QUESTION 2:
Consider a check–out station at a small store with customer
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customers per hour. There are two service team members, Tom and
Jerry, working one per shift. In Tom’s shift, the service times are
exponentially distributed with the mean time equal to 3 minutes,
while for Jerry service times are exponentially distributed with
the mean time equal to 5 minutes.
1. Find the mean queue length during the...
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