HandSimulation - QUEUEING SYSTEMS Queueing Systems...

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Unformatted text preview: QUEUEING SYSTEMS Queueing Systems Population Server Waiting Line (Queue) Entities Finite vs. Infinite One line vs. Multiple lines One server vs. multiple server Characteristics Interarrival and Service Times Exponential (M) Deterministic (D) Erlang (E) General (G) Queue discipline First Come/In First Served/Out (FCFS/FIFO) Last Come/In First Served/Out (LCFS/LIFO) Earliest Due Date (EDD) System Capacity Number of Servers Applications System Entity Server Hospital Patient Doctor, Nurse Manufacturing Customer order Machine Food Store Purchased grocery Cashier Bank Client Clerk Computer Job CPU or disk Communication Link Data Package Data Channel Analysis Methods Queueing Theory (Analytical) Simulation Performance Measures Average Waiting Time Maximum Waiting Time Average Number of Entities in the System Maximum Number of Entities in the System Server Utilization Average System Time Maximum System Time Spreadsheet Example M/U/1 Simulation : Determine waiting time in queue Lindleys Formula WQ i : waiting time in queue for customer i S i : service time for customer i IA i : interarrival time between customers i-1 and i ) , max( 1 1 i i i i IA S WQ WQ- + =-- Hand Simulation of G/G/1 Events: Arrival Event entry of a unit into the system Departure Event completion of service on a unit End Event end of simulation Variables: Q(t) : number of units in queue at time t B(t) : number of units in server at time t L(t) = Q(t) + B(t) : number of units in system at time t Arrival event Schedule next arrival Increase number in the system Set service time & schedule departure Increase entity number in queue Make server busy Is server busy? NO YES L(t)=L(t)+1 Q(t)=Q(t)+1 B(t)=1 Departure event Decrease number in system Set service time & scheduled departure for entity in service Make server idle Decrease number in queue Is queue empty? NO YES L(t)=L(t)-1 Q(t)=Q(t)-1 B(t)=0 System Clock B ( t ) Q ( t ) Arrival times of custs. in queue Event calendar Number of completed waiting times in queue Total of waiting times in queue Area under Q ( t ) Area under B ( t ) Q ( t ) graph B ( t ) graph Time (Minutes) Interarrival times 1.73, 1.35, 0.71, 0.62, 14.28, 0.70, 15.52, 3.15, 1.76, 1.00, ......
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HandSimulation - QUEUEING SYSTEMS Queueing Systems...

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