1. Queuing

2. Elements of Waiting Lines  Population –Source of customers Infinite or finite

3. Elements of Waiting Lines  Arrival Rate –Rate at which customers arrive at a service facility during a specified period of time –Arrivals can be defined as a Poisson distribution 

4. Elements of Waiting Lines  Service Times –How many customers can be served in a period of time –Exponential distribution The likelihood of encountering specified intervals of time or space between consecutive occurrences 

5. Eliminating an infinite queue  Arrival rate must be less than Service rate 

6. Basic Waiting Line Structures  Single-channel, single-phase Waiting line server

7. Basic Waiting Line Structures  Multiple-channel, single-phase Waiting line Servers

8.  Average number of customers in the system (waiting and being served) L = ----------- 

9.  Average number of customers in the waiting line 2 Lq = ------------------ 

10.  Average time a customer spends in the system (waiting and being served) 1 W = -----------------  -

11.  Average time a customer spends waiting in line Wq = --------------- 

12.  Probability of no customers in the system P 0 = ( 1 –  ) 

13.  Probability of n customers in the system P n = ( ) n ( 1 – ) 

14.  Utilization Rate –The proportion of time the system is in use  = 