In a single server,exponential service durations,and finite number in system model there are 4 customers in the system three in line and one being served.What is the probability no new customer will join the line? The probability of zero customers in the system is .375,arrival rate is 18 per hour and the service rate is 24 per hour.
A)0.093
B)0.1187
C)0.256
D)0.289
E)0.311

Question

Quizplus · Accepted Answer

The probability no new customer will join the line can be calculated using the birth-death process formula for a queue with a finite number of spaces. Given the probability of zero customers is 0.375 and the arrival rate (λ) is 18 per hour, and the service rate (μ) is 24 per hour, we can calculate the probability of having exactly 4 customers in the system. However, the question asks for the probability that no new customer will join, which is essentially asking for the system to not transition from state 4 to state 5 (which is not possible in this scenario since there are only 4 customers allowed in the system). The correct answer involves understanding the steady-state probabilities and the relationship between arrival and service rates, but without the need to calculate the exact probability for 4 customers. Given the information, the answer is derived from understanding the system's dynamics rather than direct calculation from the provided data.

In a Single Server,exponential Service Durations,and Finite Number in System