Modeling the Service Process
       The Kendall-Lee for Queuning
       Systems
       IENG 314: Bonus Homework
      What is Queuing Theory?
                                                                Queuing Model
       Queueing theory is the mathematical study of waiting lines, or 
       queues. 
       A queueing model is constructed so that queue lengths and 
       waiting time can be predicted. Queueing theory is generally 
       considered a branch of operations research because the results 
       are often used when making business decisions about the 
       resources needed to provide a service.
                   Queue Discipline
                    
                   The queue discipline describes the 
                   method used to determine the order in 
                   which customers are served. 
                      •    FCFS
                      •    LCFS 
                      •    SIRO 
     Erlang Distribution
     An Erlang distribution is a continuous random 
                                       1
     variable (T) whose density function f(t) is specified by 
     two parameters: a rate parameter R and a shape 
     parameter k .
                     Modeling the Service Process
                      
                      
                     We assume that the service times of different customers are independent random 
                      
                     variables and that each customer’s service time is governed by a random variable 
                     S having a density function s(t) and   be the mean service time for a customer. 
                     Then:
                      
                                               
                      
                     For example, =10  means that if customers were always present, the server could 
                     serve an average of 10 customers per hour, and the average service time of each 
                     customer would be   hour.