Package jline.api.mapqn

Class Mapqn_amva

java.lang.Object
jline.api.mapqn.Mapqn_amva
public final class Mapqn_amva extends Object
Horizontal-cut mean value analysis for a MAP server (SolverMVA method 'amva.mapqn'). Closed multiclass network of an exponential infinite-server station (think rate mu_r for class r) and one FCFS single-server station whose class-r service is the MAP (D0_r, D1_r); the MAP of class r moves only while a class-r job is in service and is frozen otherwise, the convention of SolverCTMC. The recursion walks the population lattice n <= N in lexicographic order and solves ONE linear R x R system per point. Its unknowns are the per-phase means Q_r^k = E[n_r 1{k}] over the joint phase k = (k_1..k_R), the busy laws U_r^k = P[serving r, k], the phase law pi_k and the throughputs X_r. Exact relations: the joint phase balance, the class marginals U_r = X_r E[S_r] theta_r and the per-class horizontal cut (generator balance of n_r 1{k}) of Casale-Smirni, DSN 2009. Closures: the product busy law theta_r(k_r) prod_{s != r} phi_s(k_s), phi the post-completion law of a frozen MAP, which solves the phase balance identically; the service-age closure of the cross term E[n_r 1{serving s} 1{k}] (class r accumulates at its throughput over the elapsed class-s service, whose mean given the phase is theta_s (-D0_s)^{-1} / theta_s); Little's law resolved by arrival phase with the exact FCFS response of the queue composition seen at n - e_r (the multiclass arrival theorem). K_r = 1 for every class reproduces multiclass FCFS MVA on class means. Mirrors matlab/src/api/mapqn/mapqn_amva.m and python api/mapqn/amva.py.