Discrete time queueing systems

1) Relationship between arrival and departure processes

Show the claim in 9.2.4 in the text book, That is:

{Z_n(e)}={X_n+1(e)}

{X_n(i)}={Y_n(e)}

{Y_n(i)}={X_n+1(e)}

{Z_n(i)}={Y_n+1(e)}

{X_n(d)}={X_n(e)}

{Z_n(d)}={X_n+1(e)}

2) A Bernoulli queue with limited buffer size

For a queue with:

Bernoulli arrivals: a₁(j)=a;a₀(j)=1-a

Bernoulli departures d₁(j)=a;d₀(j)=1-d

Limited buffer size C

Calculate the steady state probabitlities P(k), for early arrival and for early departure schemes