3. In an M/M/2 communication node, packets arrive according to a Poisson process of rate 18 packets per second. The system has two parallel crossbar switches, and each switch spends an exponentially distributed amount of time with mean 100 ms to process a packet. (a) Find the probability that an arriving packet must wait to be processed. (b) Find the mean number of packets in the system. (c) Find the mean time a packet spends in the system. (d) Find the probability that more than 50 packets are in the system.

1. If the values of user tool frame UT[2] is (0, 0, 0, 0, 0, 0) in the robot system, then UT[2] (a) is not activated in the robot system (b) cannot be used in recording robot point P[n] (c) coincides with default TCP frame (Def-TCP) of the robot in the robot system (d) coincides with robot world frame R in the robot system 2. A frame transformation is given as 4T; = (X,Y,Z,W,P, R) = (0,0,0, –90, 0, 90). The corresponding graphical representation of the given frame transformation is (a) (b) y y

A modem is to be designed for use over a telephone link, for which the available channel bandwidth is 6khz, and average signal to noise ratio on channel is 30db. What is the maximum error free data rate that can be supported on this channel and how many signalling state must be used? Explain the Result with reference to the channel capacity theorem.

Compute the capacity and input distribution attaining it for the discrete memoryless channel X → Y with X = y = {0, 1, 2, 3} given by Y = X + Z mod 4, where Z takes on values from Z = {0, 1, 2, 3} with z(0) = 1/2, z(1) = 0, and z(2) = z(3) = 1/4.

A Telecommunication channel in form of a copper cable has 4 kHz bandwidth. Calculate the amount of data rate that can be transmitted through this channel if binary signaling is used with raised-cosine pulses and 0.5 roll-off factor.

Suppose we get a message throughout the network using a 56,000 bits per second modem. Also suppose that we have an instruction rate of 500 MIPS in a workstation. How many instructions can the processor carry out between each message's receipt?

When one compares the waiting times in a single-phase/multiple-channel waiting linesystem with those of a multiple-phase/multiple-channel system, the averages and thevariances of waiting times of the two systems are the same. A. True B. False