a. The general continuous-time random walk is defined by Mi, -(i+i), j=i, j=i1, gij = ,...

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a. The general continuous-time random walk is defined by Mi, -(i+i), j=i, j=i1, gij = , j=i+1, 0. otherwise. Write out the forward and backward equations. b. The continuous-time queue with infinite buffer can be obtained by modifying the general random walk in the preceding problem to include a barrier at the origin. Put -20, j=0, 20, j=1, goj 0, otherwise. Find the stationary distribution assuming u j=1 < . If = and = for all i, simplify the above condition to one involving only the relative values of and . c. Repeat a and b assuming there is a boundary at j=N. Comment. a. The general continuous-time random walk is defined by Mi, -(i+i), j=i, j=i1, gij = , j=i+1, 0. otherwise. Write out the forward and backward equations. b. The continuous-time queue with infinite buffer can be obtained by modifying the general random walk in the preceding problem to include a barrier at the origin. Put -20, j=0, 20, j=1, goj 0, otherwise. Find the stationary distribution assuming u j=1 < . If = and = for all i, simplify the above condition to one involving only the relative values of and . c. Repeat a and b assuming there is a boundary at j=N. Comment.