Consider a router buffer preceding an outbound link. in this problem, you will use little’s formula, a famous formula from queuing theory. let n denote the average number of packets in the buffer plus the packet being transmitted. let a denote the rate of packets arriving at the link. let d denote the average total delay (i. e., the queuing delay plus the transmission delay) experienced by a packet. little’s formula is n = a · d. suppose that on average, the buffer contains 10 packets, and the average packet queuing delay is 10 msec. the link’s transmission rate is 100 packets/sec. using little’s formula, what is the average packet arrival rate, assuming there is no packet loss?

An external consultant recommends that a plant installs a bank of capacitors for power factor correction. this will reduce the peak electrical demand charges by an average of 93 kw every month. the plant current pays $13 per kw in peak demand charges. the capacitor bank will include 223 kw of fixed capacitors, and 183 of variable capacitors. the fixed capacitors cost $59 per kw, and the variable capacitors will cost $65 per kw. the consultant charges 21% of the equipment costs to install the capacitors. because this project will reduce the demand for the electric utility, they are prepared to provide a one-time rebate of $42 per kw of reduced demand. what is the simple payback period for this project (in years)?