Explore BrainMass

Explore BrainMass

    Queing theory

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    How do I solve a formula or equation for the Erlang System M/G/s/GD/s/infinity that predicts resource requirements (how many servers) using the known variables (1) new events per unit of time; (2) average time per event; (3) event time service level (must be resolved by duration); (4) percent of events that must meet that event time service level (duration).

    © BrainMass Inc. brainmass.com November 24, 2022, 11:33 am ad1c9bdddf

    Solution Preview

    Let us consider the queuing system for which
    a(t)=rl(rlt)^(r-1)*e^(-rlt)/(r-1)!, t>=0 (1)
    b(x)=ue^(-ux) x>=0 (2)
    When we find k customers in this system and when arriving customer is in the ith stage of arrival(1<=i<=r) then the total number of stages of arrival in the system is given by

    Let us use P(j)=Prob[j stages in system] so that P(j) is defined to be the number of arrival stages in the system. As always p_(k) will be the equilibrium probability for number of customers in the system, and clearly they are related through
    p_(k)=P(rk)+P(rk+1)+...+P(r(k+1)-1). (**)

    The system we have defined is an irreducible ergodic Markov chain with its state-transition-rate diagram for stages given below

    Solution Summary

    This shows how to solve a formula for the Erlang System M/G/s/GD/s/infinity that predicts resource requirements using given variables.