1. Demo on Queuing Concepts
Refer to handout on web page.
Basic queuing system: Customers arrive to a bank, they
will wait if the teller is busy, then are served and leave.
Scenario 1: Constant interarrival time and service time
Scenario 2: Variable interarrival time and service time
Objective: To understand concept of average waiting time, average number in line, utilization, and the effect of variability.
IE 429, Parisay, January 2010

2. Scenario 1: Constant interarrival time (2 min) and
service time (1 min)
Scenario 2: Variable interarrival time and service time

3. Queuing Theory Arrival process Service process Queue Discipline
Chap. 20, page 1051
Queuing Theory
Arrival process
Service process
Queue Discipline
Method to join queue
IE 417, Chap 20, Jan 99

4. Queuing Theory Basic queuing system: Customers arrive to a bank, they
will wait if the teller is busy, then are served and leave.
Assume:
Interarrival times ~ exponential
Service times ~ exponential
E(service times) < E(interarrival times)
IE 429, Parisay, January 2010

5. Each Distribution for Random Variable Has:
Definition
Parameters
Density or Mass function
Cumulative function
Range of valid values
Mean and Variance
IE 417, Chap 20, Jan 99

6. Triangular Distribution

7. Normal Distribution
EGR 549

8. Continuous Uniform Distribution
f(x) a b
F(x) a b
EGR 549

9. Exponential Distribution.
= mean interval between consequent events
= rate = mean number of counts in the unit interval > 0
X = distance between events >0
f(x)
F(x)
EGR 549

10. Notations used for QUEUING SYSTEM in steady state (AVERAGES)
= Arrival rate approaching the system
e = Arrival rate (effective) entering the system
= Maximum (possible) service rate
e = Practical (effective) service rate
L = Number of customers present in the system
Lq = Number of customers waiting in the line
Ls = Number of customers in service
W = Time a customer spends in the system
Wq = Time a customer spends in the line
Ws = Time a customer spends in service
IE 417, Chap 20, May 99

11. Notations used for QUEUING SYSTEM in steady state
j = State of the system, number of people in the system
= Traffic intensity = /
= P(j) = Probability that j units are in the system
= P(0) = Probability that there are no units (idle)
in the system
Pw = P(j>S) = Probability that an arriving unit has
to wait for service
C = System capacity (limit)
= Probability that a system is full (lost customer)
= Probability that a
particular server is idle
EGR549, Chap 20, May 2012