Queuing models
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Transcript of Queuing models
The Fundamentals
Collection of entities kept in order Addition of entity at the rear of the terminal
and removal at the front terminal
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
Population Arrival Service/Servers Queue Output
FIFO (First in First out) LIFO (Last in First out) SIRO (Serve in Random
Order) Priority Queue
Parallel Series
Customers in line
servers
Customers waiting in line
servers
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
Customer Averages:W = expected time spent in the systemWQ = expected time spent in the queue
WS = expected time spent in service
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
= arrival rate1/= mean time between arrivals
= service rate1/= mean service time per customer
= traffic intensity = / x 100 = % service utilization
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
30 customers per hour = 0.5 cx/min
1.5 mins/cx = 1 cx / 1.5 mins/cx = 0.67 cx/min
Excel File
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
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
Thank you