Operations Research20795 marksNumerical: M/M/1 queuing modelAverage number of customers in system and queue
On the average 96 patients per 24 hours day require the emergency service in clinic. Also on the average, a patient requires 10 minutes of active attention. Assume that the facility can handle only one emergency at a time. If this situation satisfies all the conditions for apply queuing theory, find
On the average 96 patients per 24 hours day require the emergency service in clinic. Also on the average, a patient requires 10 minutes of active attention. Assume that the facility can handle only one emergency at a time. If this situation satisfies all the conditions for apply queuing theory, find the average (expected) queue length and the waiting time for the patient to be served. [5]
- Arrivals: 96 patients per 24-hour day - Service time per patient: 10 minutes (active attention) - Single server (one emergency at a time) - M/M/1 conditions satisfied Arrival rate: $$\lambda = \frac{96}{24 \text{ hr}} = 4 \text{ patients/hour}$$ Service rate (10 min per patient means 6 per hour...