Operations Research2080.25 marksNumerical: M/M/1 queuing modelOperating characteristics of queuing systems
A TV repairman finds that the time spent on his job has an exponential distribution with mean 30 minutes. If he repairs sets in the order in which they come and if the arrival of sets is approximately Poisson with an average rate of 10 per 8 hour day. What is his expected idle time each day? How man
A TV repairman finds that the time spent on his job has an exponential distribution with mean 30 minutes. If he repairs sets in the order in which they come and if the arrival of sets is approximately Poisson with an average rate of 10 per 8 hour day. What is his expected idle time each day? How many jobs are ahead of the set just brought in? [5]
- Service time: Exponential, mean = 30 minutes - Arrival: Poisson, average rate = 10 sets per 8-hour day - Working day = 8 hours = 480 minutes Service rate: mean service time 30 min = 0.5 hour, so $$\mu = \frac{1}{0.5} = 2 \text{ sets/hour}$$ Arrival rate: $$\lambda = \frac{10}{8} = 1.25 \text{ s...