number of bottles being recycled average waiting time of the customers\' increas
ID: 3356963 • Letter: N
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number of bottles being recycled average waiting time of the customers' increases The waiting line models discussed in class assume FCFS, random arrivals of customers, limited capacity, and random process times. An entity is what provides the service while the service time is the time to complete the task. Waiting line economic models balance waiting cos with sales volume. 2. 8. 9. Disney's Fastpass is a virtual queue system. 10. Time waiting for a service depends on two factor 3. the volume of customers and the location of the resources 4. Waiting line models describe the steady-state operating characteristics of a waiting line. Problem 1 (Questions 11-15) An airport has a single runway for landings. The time between airplane arrivals (inter-arrival time of landings) is 12 minutes and each landing requires about 8 minutes (service time). Select the option closest to your result a) 6796; b) 50%, c) 75%; d) 58% a) 0.81; b) 2.19; c) 0.50; d) 1.33 a) 16.0; b) 26.3; c) 9.7; d) 6.0 a) 50% b) 25% c) 33% d) 42% 1.How busy is the runway? 2.What is the average number of airplanes waiting to land? 3. What is the average waiting time per plane (in minutes)? 4. What is the probability there are no planes waiting to land? 5. What is the probability there are 2 or more planes waiting to land? a) 44%, b) 25%, c) 56%, d) 34%Explanation / Answer
: mean rate of arrival = 1/12 = 0.0833
µ: mean service rate = 1/8 = 0.125
1. Utilization = 8/12 = 0.6667 = 67% (option A)
2.
Lq: mean number of customers in the queue
Lq = (1/12)^2 / ((0.125*(0.125 - 1/12))) = 1.3333
Option (D)
3.
Wq: mean wait in the queue
Wq = 1.33/(1/12) = 15.96 mins
Option (A) is correct
4.
P0 = 1 - 0.6667 = 0.3333
P1 = (0.6667)^1*0.3333 = 0.2222
Required probability = 1 - P0 - P1 = 1 - 0.3333 - 0.2222 = 0.4445
Option A is correct
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