Download Performance Evaluation cheatcheat and more Cheat Sheet Performance Evaluation in PDF only on Docsity! Little’s Law: • Little’s Law overall station: • Little’s Law queue only: E[N]: expected # customers& E[R]: response time & Labda: expected # customers arriving per unit time. DTMC: Limiting distribution: (not always exist!) exist when: & Recurrent states: return probability 1 (1-2 & 7 & 8-10) Transient (nonrecurrent): non-zero chance not returning to this state (3-6) Absorbing: probability state to self is 1 (7) Period: greatest common divisor, if from state how many steps to get back. State probability distribution after n steps: CTMC: → q_i = how long in state, p_i = probability stransition from state When in state i, probability going to state j within small amount of time h: Generator matrix Q: count going out of state to other state, amount going in said state = negative (so total add up to 0) Steady state: & Period: no issue, reducibility is GBE: look at states, flux in = flux out MM1 queue: & || E[A] = exp interarrival times, E[S] expected service time [Left CTMC i.e. constant rates]: GBE -> steady state dist → ^where p0: → & & normalization pi, we find: Mean jobs E[N] then: & mean response time E[R] then: Pr {R <= t}, , given erlang N distribution: [Right CTMC, non-constant rates]: , then: where p0: Mean # jobs in system E[N]: , mean response time: MMm queue: , Steady state dist: , Pr {waiting}: , w/ p0 = ↑ MM∞: , , then , , mean # jobs E[N] = rho MM1m: , MMmm: , w/ MMmm queue w/ trunk reservation: K system users, issue job, think time Z, E[Z] = 1/labda. Job service time E[S]= 1/mu Mean jobs: MM1 q: . Where Lq is average # customers waiting in line: , with steady-state expected waiting time: e.g. max size MM4/9 q: 9-4 = 5 MM3 q: 10 arrival per hour, w/ mean service time10 mins, traffic intens: MD1 q: , , MG1: , Arrival + processing given, max arrival w_q <=3, MM1 q:
