Question: Suppose, there is a queue A having i customers initially. The service time of the queue is Exponentially distributed with parameter $\mu$ (i.e., mean service time of one customer in Queue A is 1/$\mu$). Arrival to queue A has Poisson distribution with mean $\lambda$. What is the expected time before queue A becomes empty […]

Given a Poisson process (e.g. radioactive decay) with rate $\lambda$, then the expression $\exp(-\lambda t)$ is the probability of observing no counts in time interval $t$. This can be interpreted (after normalization) as the probability distribution (exponential distribution) of time intervals during which no counts are observed. It is often said that this can also […]

Given one lane for turning left and one lane for thru traffic. Cars arrive according to a Poisson process with rate $\lambda = 20$ per minute. An arriving car turns left with ${40\%}$ probability, and wants to go straight with 60% probability. The left-hand turn lane has a max capacity of $10$ cars. If more […]

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