queuing project

7/27/2019 Queuing Project

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Queuing Systems Findings

Team 4



Challenges

• Access to real world examples

• When does service begin and end for each

unit?

• Time constraints and accuracy of observations

• Limitations of charts



Single Line Single ServerObservation: Newark Grade School Lunch Line

• Served Monday-Friday from 11:30 to 1PM

• Roughly 288 students served per day

• Students get their finger scanned before they are

served lunch. The time it takes to process a student’s

finger print once the lunch tray is at hand is the basis

of our service time calculation

•24 samples per day, for threedays, for a total of 72 observations



Single Line Single Server

(Selected Queue Metrics)

• (μ) = 7 students per minute

• (λ) = 3 students per minute

•

(ρ) = 3/7 = 42.86%• (Ρ0) = (1 – .4286) (.4286)0 = .5714 * 1 = 57.14%

• (Lq) = 32 / 7(7-3) = 9 / 28 = .32 units

• (Wq

) = .32/3 = 11 = 6.4 seconds

• (Ls) = 3 / 7 - 3 = 3 / 4 = .75 units

• (Ws) = .75/3 = .25 = 15 seconds



Single Line Multiple ServerObservation: Walgreens

• Our only night time observation, from 10:30PM to

12AM

• Large pharmacy and retail chain

• One single line behind multiple cash registers

• Measurements based on

service time at cash register



Single Line Multiple Server

(Selected Queue Metrics)

• (μ) = 28 customers per hour

• (λ) = 48 customers per hour

•

(λ/ μ) = 48/28• (Lq) = 5.2586 units

• (Wq) = 5.256/48=.109554 hours

• (Ls

) = 5.2586+1.7=6.9586 units

• (WS) = 6.9586/48=.144971 hours

• (Pw) =Pw = Lq((Sµ/ λ)-1) = 0.876433



Constant Service RateObservation: Magic Car Wash & Lube

• Data collected on a Saturday from 10AM to 12PM

• Deals with lubricants and both interior and exterior

washing

• 20 cycles viewed



Constant Service Rate(Selected Queue Metrics)

• (μ) = 12 cars per hour

• (λ) = 15 cars per hour

• (ρ) = 12/15 = 80%

• (Ρ0) = (1 – .8) (.8)0 = .2 * 1 = 20%

• (Lq) = Lq = λ^2/ 2μ(μ- λ) = 12^2/ 2(15)(15-12) = 1.6cars

• (Wq) =

• (Ls) = Ls= Lq + λ/μ = 1.6 + (12/15) = 2.4 customers

• (Ws) =



Finite PopulationObservation: Printer Repair Service at S&P’s

• Printer frequently goes off line due to jams, lack of

paper or other technical problems

• Calculations were based on the time it takes in

between print job failure to the time it takes to getback on line



Finite Population

(Selected Queue Metrics)• (N) = 5 printers***• (S) = 1 past observation

• (T) = 62 minutes per day

• (U) = 433 minutes per day

• (X) = 62/(62+433)=.125

• (F) = .92

• (J) = NF(1-X)=5*0.920(1-0.125)=4.0250

•

(H) = FNX=0.920*5*0.125=0.5750• (Po) = 1 – λ/ µ = 1 – 0.2/0.25 = 0.2

• (Pn) = N!/(N-n)!X^nPo, where n equal 0 = 0.2

•

(Pw) = 1 – Pn = 0.8 = 80%

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