krm8_ism_c - Supplement C Waiting Lines PROBLEMS 1....

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Unformatted text preview: Supplement C Waiting Lines PROBLEMS 1. Solomon, Smith and Sanson a. Single-server model, average utilization rate. 8 0.8 10 = = = or 80% utilization b. The probability of four or fewer documents in the system is 0.6723 as shown following. Therefore, the probability of more than four documents in the system is 1 0.6723 = 0.3277. ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 4 4 3 3 2 2 1 1 1 1 0.8 0.8 0.0819 1 0.8 0.8 0.1024 1 0.8 0.8 0.1280 1 0.8 0.8 0.1600 1 0.8 0.8 0.2000 0.6723 n n P P P P P P =- =- = =- = =- = =- = =- = = c. The average number of pages of documents waiting to be typed, 8 8 3.2 pages 10 10 8 q L L = = = = -- 2. Bennys Arcade Because there are only six machines, we must use the finite source model. a. To calculate the Jimmys utilization, we need to compute the probability that he will have no machines to repair. 1/50 0.02 = = machines per hour 1/15 0.0667 = = machines per hour ( 29 1 6 6! 0.02 6 ! 0.0667 n o n o P n- = = - [ ] 1 13.92 0.0718- = = = Jimmys utilization 1 0.0718 0.9282 = - = 173 l PART 2 l Managing Processes b. Average number of machines out of service. ( 29 0.0667 6 1 0.0718 6 3.095 2.905 0.02 =-- =- = L machines c. Average time a machine is out of service. ( 29 ( 29 2.905 6 2.905 0.02 46.93 =- = W hours 3. Moore, Akin, and Payne (dental clinic). Multiple-server model. 3 = s , 5 = , 2 = , ( 29 5 0.8333 3 2 = = = s a. Probability of no patients, = P ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 [ ] ( 29 { } ( 29 ( 29 1 1 1 2 5 6 1 1 2 3 5 6 1 5 2 5 2 1 1 ! ! 1 ! 3! 1 5 2 5 2 5 2 5 2 1 0! 1! 2! 3! 1 1 2.5 3.125 2.604 6 1 0.04494 6.625 15.625 n s n s s n n P n s n --- = =-- = + = + -- = + + + - = + + + = = + b. The probability of 6 or more customers in the clinic is: 0.04494 P = (from part a), s = 3 for n s < ( 29 ( 29 ( 29 ( 29 ( 29 1 5 2 1 2 5 2 2 ! 0.04494 0.11235 1! 0.04494 0.14044 2! n n P P n P P = = = = = for n s ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 3 5 2 3 4 5 2 4 1 5 5 2 5 2 ! 0.04494 0.11703 3!3 0.04494 0.09753 3!3 0.04494 0.08127 3!3 n n n s P P s s P P P - = = = = = = = ( 29 ( 29 1 2 3 4 5 1 1 0.04494 0.11235 0.14044 0.11703 0.09753 0.08127 0.40644 P P P P P P- + + + + + = - + + + + + = Waiting Lines l SUPPLEMENT C l 174 c. The average number of patients waiting in the lobby, ( 29 ( 29 ( 29 ( 29 ( 29 3 5 5 2 6 2 2 1 5 6 6 0.04494 0.58516 3.5109 ! 1 3! 1 s q P L s = = = =-- d. The average time spent in the clinic, W = 1 1 3.5109 1 1.2022 5 2 q q L w + = + = + = hours...
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This note was uploaded on 12/19/2009 for the course MANAGEMENT 00123 taught by Professor Ahmed during the Spring '09 term at Albany College of Pharmacy and Health Sciences.

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krm8_ism_c - Supplement C Waiting Lines PROBLEMS 1....

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