Final answer:
To find the expected number of lost arrivals in a one-hour interval, we first need to find the expected number of arrivals in one hour using the Poisson process. The rate of arrivals is given as 1 per minute, so in 60 minutes, we expect 60 arrivals in total. We can then calculate the expected number of arrivals that find two jobs in the system and are therefore lost by multiplying the probability of there being two jobs in the system by the expected response time.
Step-by-step explanation:
To find the expected number of lost arrivals in a one-hour interval, we first need to find the expected number of arrivals in one hour using the Poisson process. The rate of arrivals is given as 1 per minute, so in 60 minutes, we expect 60 arrivals in total.
Next, we need to determine the expected number of arrivals that find two jobs in the system and are therefore lost. If there is one job in the system, the processing time is exponentially distributed with a mean of 40 seconds. If there are two jobs in the system, the processing time is exponentially distributed with a mean of 20 seconds.
Let's denote the probability of there being one job in the system as P(1), and the probability of there being two jobs in the system as P(2). The expected number of arrivals that find two jobs in the system and are lost can be calculated as:
E(Loss) = P(2) * E(RTT)
where E(RTT) is the expected response time. For one job in the system, E(RTT) = 40 seconds, and for two jobs in the system, E(RTT) = 20 seconds. We can find P(1) and P(2) using Little's law:
P(1) = E(J) / E(T)
P(2) = P(1)^2
where E(J) is the expected number of jobs in the system and E(T) is the expected response time.