Application of Queueing

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Presentation transcript:

Application of Queueing Decision Making – Controllable Parameters Number of servers at a service facility (s) Efficiency of servers (m) Number of service facilities Arrival rate of customers (l)

Application of Queueing Decisions have a cost: Cost of service

Application of Queueing Decisions have a cost: Cost of waiting

Application of Queueing Decisions have a cost: Total Cost

Application of Queueing Approaches for Minimizing Total Cost Typically there are a limited number of scenarios. Therefore find the total cost for each combination. Ex. How many cashiers at grocery? You know the cost per hour for each cashier (service cost) and can observe service (m) and arrival (l) rates. May be difficult to estimate cost of waiting (note extreme case in Soviet Union). Can determine L and W for different levels of s, and corresponding costs.

Application of Queueing Example: Problem 21 Current copy machine rate (15copies / minute) Faster machine rate (45 copies / minute) Customer service time ~ EXP(2 minute service time, or rate of 30 cust / hour). Of this time, 1.5 minutes are for setup and .5 minutes for copying) Therefore with faster machine, service time is 1.5 + .166666 = 1.666666 minutes (or a rate of 36 cust. / hour). 24 customers arrive per hour

Application of Queueing Example: Problem 21 1-Fast Machine 2-Original Machines M/M/1 M/M/2 = 36 cust / hour m = 30 cust / hour = 24 cust / hour l = 24 cust / hour r = l/2 m L = r/(1-r) = 2 L = r+(2r3/(1-r2)) = 0.55 W = L/l = 2/24 = .083 hours W = 0.55/24 = .023 hours Cost = Serv. Cost + Wait Cost Cost / hour = (k2 + .083k3) Cost / hour = (2k1 + .023k3)

Waiting for Practicality Article