210x Filetype PPTX File size 0.25 MB Source: www.umich.edu
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
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