Priority :Average Arrival Rate (exponential interarrival times)
High : 3 per hour
Low : 5 per hour
Number of servers: 5
Service rate: 2 per hour (exponential service times)
-What is the average time in line (in minutes)for a low priority item?
A)2
B)5
C)24
D)35
E)54

Question

Priority :Average Arrival Rate (exponential interarrival times)
High : 3 per hour
Low : 5 per hour
Number of servers: 5
Service rate: 2 per hour (exponential service times)
-What is the average time in line (in minutes)for a low priority item?
A)2 
B)5 
C)24 
D)35 
E)54

Quizplus · Accepted Answer

To find the average time in line for a low priority item, we need to use Little's Law, which states that the average number of items in a system (L) is equal to the arrival rate (λ) multiplied by the average time in the system (W). We can calculate the arrival rate for low priority items as 5 per hour. The service rate is 2 per hour, so the average time in the system (including service time and wait time) is 1/3 hour (20 minutes) per item. Therefore, using Little's Law, we can calculate the average number of low priority items in the system as L = λ * W = 5 * 1/3 = 5/3. Since there are five servers, it means the average time in line is given by (5/3 - 5) / (5 * 2) = - 4/30 = -0.133 hours or -8 minutes, which means that there is actually no waiting line for low priority items. Thus, the best choice is C (no waiting line)

Priority :Average Arrival Rate (Exponential Interarrival Times)