Router design

Packets at the UM gateway arrive according to a Bernoulli process with parameter 0.12. The time is slotted in microseconds. Assume that all packets have the same length of 1 MB. A router requires at least one standard microprocessor with a memory stack. Assume that each standard microprocessor can provide service with service time that is geometrically distributed with the expected value of 35 microseconds and comes with a memorystack that can store 100 MB. The following specifications need to be satisfied in steady-state: (a) Expected wait time for each new packet before service begins is no longer than 75 microseconds and (b) Probability of buffer overflow is less than 10 2. A router with multiple processors splits the arrival process probabilistically with parallel connections. Find the minimum number of processors required to satisfy the specifications