1. 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)

2. Application of Queueing
Decisions have a cost: Cost of service

3. Application of Queueing
Decisions have a cost: Cost of waiting

4. Application of Queueing
Decisions have a cost: Total Cost

5. 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.

6. 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 = minutes (or a rate of 36 cust. / hour).
24 customers arrive per hour

7. 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 = (k k3) Cost / hour = (2k k3)

8. Waiting for Practicality Article