queuing models
DESCRIPTION
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 PresentationTRANSCRIPT
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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