Consider the case study introduced in Section 12.2. After observing the operation of the barber shop, Herr Cutter's nephew Fritz is concerned that his uncle's estimate that the time required to give a haircut has a uniform distribution between 15 and 25 minutes appears to be a poor approximation of the actual probability distribution of haircut times. Based on the data he has gathered, Fritz's best estimate is that the actual distribution is an Erlang distribution with a mean of 20 minutes and a shape parameter of k 5 8.
a. Repeat the simulation run that Fritz previously used to obtain Figure 12.9
FIGURE 12.9: The output obtained by using the Queueing Simulator in one of this chapter's Excel files to perform a computer simulation of Herr Cutter's barber shop (without an associate) over a period of 100,000 customer arrivals.

(With a mean of 30 minutes for the interarrival-time distribution) except substitute this new distribution of haircut times.
b. Repeat the simulation run that Fritz previously used to obtain Figure 12.11
FIGURE 12.11

(With a mean of 14.3 minutes for the interarrival-time distribution) except substitute this new distribution of haircut times?

Transcribed Image Text:

Н Queueing Simulator for Herr Cutter's Barber Shop Number of Servers 95% Confidence Interval Point 4 High Estimate Low 1.385 Interarrival Times 1.358 1.332 6. Distribution Exponential 0.712 0.689 0.666 Mean 30 40.582 39.983 41.180 Wq = 20.577 19.980 21.174 Po= 10 Service Times 0.330 0.326 0.335 11 Uniform P1= P2 = P3= Distribution 0.310 0.307 0.313 12 Minimum 15 0.183 0.180 0.185 13 0.0963 0.0469 Maximum 25 0.0942 0.0920 14 0.0451 0.0433 15 Ps= 0.0220 Length of Simulation Run 0.0206 0.0192 P6= P7= Pg=| 0.00219 Pg= 0.000876 16 Number of Arrivals 100,000 0.00950 0.00849 0.0105 17 0.00503 0.00432 0.00360 18 0.00274 0.00163 19 0.000540 0.00121 Run Simulation 20 P10 = 0.000372 0.000579 0.000165 c |D |E | Queueing Simulator for Herr Cutter's Barber Shop with an Associate Н Number of Servers 95% Confidence Interval 2 Point 4 Estimate Low High Interarrival Times 2.126 2.090 2.163 Distribution Exponential Lq= 6. 0.719 0.689 0.748 Mean 14.3 30.212 29.833 30.591 Wa 10.211 9.834 10.588 9. 10 Service Times Po= 0.163 0.160 0.166 P = P2 = P3= P1= 11 Distribution Uniform 0.266 0.262 0.270 12 Minimum 15 0.233 0.230 0.235 13 Maximum 25 0.1541 0.1518 0.1564 14 0.0877 0.0855 0.0898 15 0.0487 Ps = P6 = P7=| 0.01282 Length of Simulation Run 0.0467 0.0448 16 Number of Arrivals 100,000 0.02417 0.02264 0.0257 17 0.01162 0.01401 18 0.00722 Pg= Pg= |0.003208 P10 = |0.001546 0.00634 0.00546 19 0.002530 0.00389 Run Simulation 20 0.001076 0.002017