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QUESTION

Consider an M/M/1 queue. Arrival rate is 10 customers per hour, service costs $3 per minute, and waiting costs are $0.5 per minute per customer. What...

  • Consider an M/M/1 queue. Arrival rate is 10 customers per hour, service costs $3 per minute, and waiting costs are $0.5 per minute per customer. What is the optimal service rate for this queue?
Solutionλ = 10/hrService Cost = $3/min = $180/hrWaiting Costs = $0.5 = $30/hrOptimal Service Rateµ = λ + √ λh/c= 10 + √(10*180)/30=10 + √60= 10+7.75= 17.75
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