Please can anyone help solve drivative formular on queuing theory question for me, I find it challenging.
(b) A single server queuing system provides service at a rate μ requests persecond for an arrival rate of λ requests per second.
i. State the condition for stability of this system.
ii. Give Markov birth and death model for this case.
iii. Show that the mean number of jobs in the system is ρ/(1-ρ). Calculatethe mean queue length, the server utilisation and the probability thatthe server is idle for λ= 8 jobs/sec and μ= 10 jobs/sec?
iv. Assuming that the system described above has a queuing capacity L.
(1 − ρ ) ρ i
Show that steady state probabilities are given as pi =. --------------
1 − ρ L +1
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