Chapter 18: Queuing Models

1
Chapter 18 Queuing Models
2
Capacity decisions a trade-off
Total cost
Cost of Service (provider)
Cost
Cost of Waiting (customer)
Capacity to serve
3
Model Nomenclature Terms

• A/B/C arrival dist/ service dist/ of servers
• Poisson arrivals (M)
• Distribution of independent arrivals over time
• Exponential service (M) (time between poisson
  arrivals)
• General service (G) (other distributions)

4
M/M/1
Customers waiting
Customer being served
?
µ
Lq length of queue
Ls length of ( of customers in) system

• ? average customer arrivals per hour
• µ average service rate per hour

5
M/M/1
? µ-?
Length in System (Ls)
1 µ-?
Time in System (Ws)
In an effort to maximize efficiency, the manager
of the airport tried to get the average time per
take off to equal the time between arrivals.
What will happen?
6
Definitions

• n number of customers in the system
• ? mean number of customers in system (?/µ)
• N maximum number of customers in system
• c number of servers
• Pn probability of exactly n customers in system
• L number of customers in (ssystem,qqueue,
  bbusy system)
• W mean waiting time of a customer in
  (ssystem,qqueue, bbusy system)

7
lets try one