Queuing Theory
     Queuing Systems Configurations
               Customer                                         Customer
                Arrives                                          Leaves
                                 Waiting Line      Server
                                                                 Customer
                                                                  Leaves
                                                   Server 1
                Customer                                         Customer
                Arrives                                           Leaves
                                  Waiting Line     Server 2
                                                                 Customer
                                                                  Leaves
                                                    Server 3
                 Customer                                        Customer
                  Arrives                           Server 1      Leaves
                                   Waiting Line
                  Customer                                       Customer
                  Arrives                                         Leaves
                                   Waiting Line     Server 2
                  Customer                                       Customer
                   Arrives                                        Leaves
                                    Waiting Line     Server 3
                                    -2-                               HMP654/EXECMAS
                 Queuing Theory
   Characteristics of a Queuing Process
     • Generation of Customers
         –Infinite vs. Finite calling 
           population
         –Homogeneity of the calling 
           population
         –Individual vs. Batch arrivals
         –Deterministic vs. Stochastic 
           arrivals
     • Queuing of Customers
         –Single vs. Multiple servers
         –Finite vs. Infinite queues
                      -3-                 HMP654/EXECMAS
                 Queuing Theory
    Characteristics of a Queuing Process
         –FIFO vs. LIFO disciplines
         –Priority rules
     • Servicing the Customers
         –Deterministic vs. Stochastic 
           service time
         –Individual vs. Batch Processing
                      -4-                 HMP654/EXECMAS
                 Queuing Theory
     Characteristics of a Queuing Process
     • Generation of  Customers 
         –Poisson probability distribution
                       xe
                p(x) 
                         x!
         ‘x’ represents the number of arrivals 
           in a specific time period.
         ‘’ represents the ‘arrival rate’, that 
           is, the average number of arrivals 
           per time period.
                      -5-                  HMP654/EXECMAS
                 Queuing Theory
      Arrival Rate
     The time between arrivals is known as 
        the interarrival time.  If the number 
        of arrivals in a given period follows 
        a Poisson distribution, with mean , 
        the interarrival times follow an 
        exponential probability distribution 
        with mean 1/
     The exponential distribution exhibit the 
        memoryless property.  An arrival 
        process is memoryless if the time 
        until the next arrival occurs does not 
        depend on how much time has 
        elapsed since the last arrival.
                      -6-                 HMP654/EXECMAS