Queuing models

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The Fundamentals

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The Fundamentals. Queuing models. Collection of entities kept in order Addition of entity at the rear of the terminal and removal at the front terminal. What is a queue?. Used to approximate a real queuing situation to be analyzed mathematically - PowerPoint PPT Presentation

Transcript of Queuing models

Page 1: Queuing models

The Fundamentals

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Collection of entities kept in order Addition of entity at the rear of the terminal

and removal at the front terminal

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Used to approximate a real queuing situation to be analyzed mathematically

Allow a number of useful performance measures to be determined: Average number in the queue Average time spent in queue

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Population Arrival Service/Servers Queue Output

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FIFO (First in First out) LIFO (Last in First out) SIRO (Serve in Random

Order) Priority Queue

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Parallel Series

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Customers in line

servers

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Customers waiting in line

servers

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Time Averages:L = expected no. of customers in the systemLQ = expected no. of customers in the queue

LS = expected no. of customers in service

P (all idle) = probability that all servers are idle

P (all busy) = probability that all servers are budy

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Customer Averages:W = expected time spent in the systemWQ = expected time spent in the queue

WS = expected time spent in service

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λ = average rate at w/c customers enter the system

L = expected number of customers in the systemW = expected time a customer spends in the

system

Therefore:L = λW

LQ = λWQ

LS = λWS

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= arrival rate1/= mean time between arrivals

= service rate1/= mean service time per customer

= traffic intensity = / x 100 = % service utilization

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Typical Front Desk Queuing:

30 customers per hour Each representative spends 1.5

minutes/customer Manager’s objective is to decide

whether to improve the system or not

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30 customers per hour = 0.5 cx/min

1.5 mins/cx = 1 cx / 1.5 mins/cx = 0.67 cx/min

Excel File

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M/M/s model M – means that interarrival times are

exponentially distributed M- service times for each server are

exponentially distributed s- denotes the number of servers

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Customers arrive at a rate of 150 customers per hour

Branch employs 6 tellers Average service time is 2 minutes to serve each

customer All customers performs all tasks Customers arrived and finds 6 tellers busy

serving First Come First Serve fashion Manager’s objective = to find the “best” numbers

of tellers given that tellers are paid $8 per hour

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Thank you