Inter- Time Assign- Custo Arrival Enter. ed Time RANDO Comp- Time 3 mer A (ll/ T

Question

Inter- Time Assign- Custo Arrival Enter. ed Time RANDO Comp- Time 3 mer A (ll/ Time ing Server Being Waiting for Service H (th I service letion in sys- RAND0 min) (min) Queue Served Time Time min) Time Time tem S1 S2 0.91922 1.48 0.95531 1.48 2.1 3.8 2.1 3.8 6 2 0.64513 1.48 0.7 2.4 0 0.948181 1.48 4.4 2 3.8 4.4 7 3 0.94818 1.48 4.4 4.4 0.874066 1.48 1.4 5.8 1.4 5.8 4.4 8 4 0.13757 1.48 0.1 4.5 0 0.736051 1.48 0.9 5.4 0.9 5.8 5.4 9 5 0.9 989 1.48 4.6 9.1 0 0.961458 1.48 2.2 11.3 2.2 5,8 11.3 no 6 0.85398 1.48 1.3 10.4 1 10,4 0 0.906332 1,48 1.6 1.6 1 7 0.58852 1.48 0.6 11 11 3 0.3 1,4 1.7 8 0.35853 1.48 0.3 11.3 1 1.48 2.2 14.2 2.9 14.2 9 0.990347 1.48 3.4 14.7 2 14.7 0 1.48 2.9 17.6 2.9 14.2 17.6 984131 148 28 176 28 176 17 4 10 0.13757 1.48 5 Carefully study this worksheet's table of simulation of 10 customersin a 2-server system. These numbers have been (re) constructed to mirror exactly the 6 table found in textbook in Chapter 12 (Simulation) page 576 Table 12.11. s In the next worksheet (QSIM1) the first 10 customers have exactly the same valuesas found in worksheet osuMo. You shall first enter formulasinto the yellow cells of the first 10 customer rows so that the formulas produce the same values asin QSIM0. Note that merely copying numbers from the QSIM1 will not get you any mark. After you have completed the first customers, replicate the formulas all the way uptill and including) 100th customer 2 customers from 11th to 10oth exhibited increasing arrival until peak period which sustained for a while. After that, arrival rates decreased rapidly, The 3 queue system initially responded by increasing the servers. But there was some lag. Later, again after abitoflag, the system noted the 4 decreasing arrival rates and correspondingly decreased the service rates to match 6 that you have the results of simulation, complete the assignment by entering the calculations in the summary cells at the bottom, such as finding the Now

Explanation / Answer

(i) Inter arrival Time will be calculated by using mean = 1.48

c.d.f of exponential distribution = 1 - e -x = RAND()

so Inter arrival Time (min) = - (1/) [ ln ( 1 - RAND()] by applying this formula we will get the given excel column values

(ii) Time entering queue = Cumulative values of Interarrival time

like for first customer it would be = interarrival time (1)

for second customer, it would be =  interarrival time (1) + interarrival time (2)

or third customer, it would be =  interarrival time (1) + interarrival time (2) +interarrival time (2) and so on

(iii) Assigned Server ( either 1 or 2 )

It will be assigned by the value whichever value is lesser among S1 and S2 in its previous row ( given in last columns) . Like for

Customer No.3 S1 = 3,8 ( in row 2 ) and S2 = 4.4 ( in row 2) so 1 will be choosen for S1

Customer No.9 S1 = 14.2 ( in row 8 ) and S2 = 13 ( in row 8) so 2 will be choosen for S2

(iv) Time being served at kthrow is Calculated by taking Max[ Time Entering queue (in kthrow) , min(S1, S2 ) ( in k-1th row) ]

for

Customer No.6 Time being served at 6th row= Max[ Time Entering queue (in 6th row) , min(S1, S2 ) ( in 5th row) ] = Max[ 10.4, min (5.8, 11.3) ] = Max[ 10.4, 5.8] = 10.4

Customer No.7 Time being served at 7throw= Max[ Time Entering queue (in 7throw) , min(S1, S2 ) ( in 6th row) ] = Max[ 11, min (12 11.3) ] = Max[ 11, 11.3] = 11.3

Customer No.8 Time being served at 8throw= Max[ Time Entering queue (in 8throw) , min(S1, S2 ) ( in 8th row) ] = Max[ 11.3, min (12, 13) ] = Max[ 11.3,12] = 12

(V) Waiting Tme = Time being served ( column (iv)) - Arrival Time (column (ii)

(Vi) Service time is also calculated similarly as we calculated waiting time

Service Time will be calculated by using mean mu = 1.48

c.d.f of exponential distribution = 1 - e -x = RAND()

so Inter arrival Time (min) = - (1/ ) [ ln ( 1 - RAND()] by applying this formula we will get the given excel clumn values.

(vii) Completion Time in ithrow = Service time + time being served, both in ithrow.

(viii) Time in system in ithrow = Service time + waiting time, both in ithrow.

(ix) S1 ( in ithrow ) = Completion time if Assigned server value column is 1

= S1 of (i-1)th row

(x) S2( in ithrow ) = Completion time if Assigned server value column is 2

= S2 of (i-1)th row

I have provided all the formulas you required in the given problem.

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