91影视

In this problem, we are given the Poisson arrival rate 位 = 2, the number of servers n = 3, and the service distribution as uniform over the interval (0, 2).

Since the service distribution is uniformly distributed over the interval (0, 2), we can obtain the average service rate (碌) as the midpoint, which is \(\frac{0+2}{2}\), giving us 碌 = 1.

Traffic intensity (蟻) is the ratio of arrival rate to the average service rate times the number of servers: \(蟻 = \frac{位}{n \cdot 碌}\). We plug in the given values and compute the traffic intensity: 蟻 = \(\frac{2}{3 \cdot 1}\) = \(\frac{2}{3}\)

Using the Erlang B formula for loss systems, we can find the probability of all servers being busy (P_loss) when a customer arrives. The Erlang B formula is given as: \[P_loss(E, n) = \frac{\frac{(E^n)}{n!}}{\sum_{k=0}^n \frac{(E^k)}{k!}}\] where \(E = 蟻 \cdot n\) is the offered load and n is the number of servers. Plug in the values: E = \(\frac{2}{3} \cdot 3\) = 2 Let's compute the numerator and denominator separately: Numerator = \(\frac{2^3}{3!} = \frac{8}{6}\) Denominator = \(\frac{1}{0!} + \frac{2^1}{1!} + \frac{2^2}{2!} + \frac{2^3}{3!} = 1 + 2 + 2 + \frac{8}{6}\) Now, compute P_loss: \[P_{loss} = \frac{\frac{8}{6}}{1 + 2 + 2 + \frac{8}{6}} = \frac{\frac{8}{6}}{5 + \frac{8}{6}} = \frac{8}{16}\] The proportion of potential customers who are lost is P_loss = \(\frac{1}{2}\), or 50%.