Queueing theory
Budget: $10 – $30 USD
I am looking for an experienced mathematician in Queueing theory
(a) Consider an M/M/∞ (self-service) model with arrival and service rates
λ and µ respectively.
(i) Give one example of real-world situations in which this model is applicable to.
(ii) Show that the steady state probabilities follow Poisson distribution with
parameter ρ := λ/µ.
(iii) Compute the performance measures L, Lq, W and Wq of the system.
Hint: Note that λn = λ, n = 0, 1, 2, ... and µn = nµ, n = 0, 1, 2, ...
(b) Let {N(t), t ≥ 0} be a Poisson process with rate λ that is independent
of the nonnegative random variable X with mean µ and variance σ^2
. Find
(i) Cov(T, N(T)).
(ii)Var(N(T)).
(a) Consider an M/M/∞ (self-service) model with arrival and service rates
λ and µ respectively.
(i) Give one example of real-world situations in which this model is applicable to.
(ii) Show that the steady state probabilities follow Poisson distribution with
parameter ρ := λ/µ.
(iii) Compute the performance measures L, Lq, W and Wq of the system.
Hint: Note that λn = λ, n = 0, 1, 2, ... and µn = nµ, n = 0, 1, 2, ...
(b) Let {N(t), t ≥ 0} be a Poisson process with rate λ that is independent
of the nonnegative random variable X with mean µ and variance σ^2
. Find
(i) Cov(T, N(T)).
(ii)Var(N(T)).