Wilshire Clinic has sixteen clinicians. Currently, the arrival rate for each cli

Question

Wilshire Clinic has sixteen clinicians. Currently, the arrival rate for each clinician is 6 patients per hour and the service rate for each clinician is 8 patients per hour. Both interarrival time and service time are exponentially distributed.
    Suppose each clinician serves his or her own patients. Use Exhibit_7.12.

What is the utilization rate of a clinician? (Round your answer to 4 decimal places.)

What is the average waiting time in line? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

To improve patients' experience, Wilshire Clinic decides to divide sixteen clinicians into four teams, each of which consists of 4 clinicians. A patient's information is shared within the team, so a clinician can serve a patient who comes to any clinician on the same team.

What is the average number of patients waiting in line for each team? (Round your answer to 4 decimal places.)

Wilshire Clinic has sixteen clinicians. Currently, the arrival rate for each clinician is 6 patients per hour and the service rate for each clinician is 8 patients per hour. Both interarrival time and service time are exponentially distributed.
    Suppose each clinician serves his or her own patients. Use Exhibit_7.12.

Explanation / Answer

Wilshire Clinic has sixteen clinicians. Currently, the arrival rate for each clinician is 6 patients per hour and the service rate for each clinician is 8 patients per hour. Both inter arrival time and service time are exponentially distributed. Suppose each clinician serves his or her own patients.

a. What is the utilization rate of a clinician?

Arrival rate a = 60/6 = 10 mins,

p = 60/8 = 7.5 mins, m=1.

Utilization for multiple resources (u) = p/(a * m) = 7.5/(10 * 1) = 0.75

b. What is the average waiting time in line?

Time in queue (tq)

= (activity time / m) * ((utiltization^(sqrt(2(m+1))-1)) / (1 - utilization)) * ((CVa^2 + CVp^2)/2)

CVa=CVp=1.So, using the queueing formula,

we obtain Tq= 30 minutes

To improve patients' experience, Wilshire Clinic decides to divide sixteen clinicians into four teams, each of which consists of 4 clinicians. A patient's information is shared within the team, so a clinician can serve a patient who comes to any clinician on the same team.

c. What is the arrival rate for each team?

6*4 = 24 customers/hour

d. What is the utilization rate of a clinician?

p = 60/8 = 7.5 mins, m=1.

Arrival rate a = 60/24 = 2.5 mins,

u= p /(a * m)

= 7.5 / (2.5 * 1) = 3 min

e. What is the average waiting time in line?

CVa=CVp=1. So, using the queueing formula (mentioned above)

we get Tq=11.25 mins

f. What is the average number of patients waiting in line for each team?

Using Little’s Law,

Iq=Tq/a

=11.25 / 2.5 = 4.5

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