Question

Huduko Inc. offers a number of computer services. Huduko operates with a utilization of 30 percent. The interarrival time of jobs is 8 milliseconds (0.008 second) with a coefficient of variation of 1.5. On average, there are 20 jobs waiting in the queue to be served and 60 jobs in process (i.e., being processed by a server rather than waiting to be sent to a server for processing).

Required:
How many servers do they have in this system?

Answer 1

To determine the number of servers in the system, we need to calculate the potential number of jobs in the queue and being processed. Using the arrival rate and service rate, we can calculate the average number of jobs in the system. Given the information provided, Huduko Inc. has approximately 38 servers in the system.

Step-by-step explanation:

To determine the number of servers in the system, we need to calculate the potential number of jobs in the queue and being processed. The average number of jobs waiting in the queue is given as 20, and the number of jobs being processed is given as 60. Therefore, the total number of jobs in the system is 20 + 60 = 80.

Since the system operates with a utilization of 30 percent, the average number of jobs in the system can be calculated using the formula L = λ * W, where L is the average number of jobs in the system, λ is the arrival rate, and W is the average time a job spends in the system. Rearranging the formula, we have L = λ / μ, where μ is the service rate.

Given that the interarrival time of jobs is 8 milliseconds (0.008 seconds) and the coefficient of variation is 1.5, we can calculate the service rate as μ = 1 / (0.008 * 0.3). Therefore, the average number of jobs in the system is L = (1 / (0.008 * 0.3)) * 0.008 = 41.67.

Since we already have 80 jobs in the system, the number of servers can be found by subtracting the average number of jobs in the system from the total number of jobs in the system. Therefore, the number of servers is 80 - 41.67 = 38.33. As the number of servers cannot be a fraction, we can conclude that Huduko Inc. has approximately 38 servers in the system.

Answer 2

Huduko Inc.

The number of servers in this system is:

= 200.

Step-by-step explanation:

a) Data and Calculations:

Utilization rate = 30%

Interarrival time of jobs = 8 milliseconds (0.008)

Coefficient of variation = 1.5

Average jobs waiting in the queue to be served = 20

Number of jobs in process = 60

Number of servers processing the 60 jobs = 60

Since the number of servers processing at a time is 60 with a utilization rate of 30%, it means that there are 200 servers in the system (60/30%).