hw8 - Homework 8 Student Name Son Tran Student ID...

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CPU 0 I/O 1 I/O m I/O 2 μ 1 μ 1 μ 1 μ 2 μ 2 μ 2 3 2 1 0 λ very fast M/M/1 Homework 8 – Student Name: Son Tran – Student ID: 2007-23576 Class: Data Networks – Spring 2008 3.61 We have = i 0mpi = 1 . The arrival rate at the CPU is λ/ p 0 and the arrival rate at the i th I/O port is λ p i / p 0 . By Jackson’s Theorem, we have , ,…, = = ( - ) Pn0 n1 nm i 0mρini 1 ρi Where = ρ λμ0p0 , and = ρi λpiμip0 for i > 0 The tandem system is as follows The arrival rate is λ. The service rate for CPU 0 is μ 0 p 0 and for I/O i th ( i = 1,. .,m) is μ i p 0 / p i . 3.64 a) The state is determined by the number of customers at node 1, when having customers at node 1, the deperture rate from node 1 is μ 1 , each departure causes the state to decrease as the figure. When customers come to node 2, the departure rate from node 2 is μ 2 , each departure causes the state to increase. b) The steady state probability at state i is p i and p i = p i-1 ρ , where ρ = μ 2 / μ 1 . So
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hw8 - Homework 8 Student Name Son Tran Student ID...

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