Fork-join (fj)

Response time of the K-way fork-join queue, order statistics and expected maxima for the common branch laws, tail latency, split-merge and serialization. More...

Collaboration diagram for Fork-join (fj):

Files
file	include/line/api/fj/fj_amva.h
	Mean value analysis of a closed network of fork-join subnetworks.
file	include/line/api/fj/fj_bounds.h
	Upper and lower bounds on the mean response time of a K-way fork-join system of M/M/1 branches.
file	include/line/api/fj/fj_branch_members.h
	Activities belonging to each branch of an AND-join.
file	include/line/api/fj/fj_char_max.h
	Gravey's characteristic maximum M_K, an upper bound on the expected maximum of K i.i.d.
file	include/line/api/fj/fj_char_max_blom.h
	Blom-corrected plotting position for the characteristic maximum.
file	include/line/api/fj/fj_char_max_discrete.h
	Characteristic maximum of a lattice random variable.
file	include/line/api/fj/fj_codes.h
	FJ_codes, the fork-join response-time-tail approximation of Z.
file	include/line/api/fj/fj_codes_matrices.h
	The state-space construction of FJ_codes, the fork-join response-time-tail approximation of Z.
file	include/line/api/fj/fj_cox_fit.h
	Two-stage Coxian fit of a mean and a squared coefficient of variation.
file	include/line/api/fj/fj_dag_makespan.h
	Makespan of a task system with precedence constraints.
file	include/line/api/fj/fj_delay_opt.h
	Deterministic subtask delays that minimise mean dispersion.
file	include/line/api/fj/fj_dispersion.h
	Mean subtask dispersion of a split-merge system with Erlang branches.
file	include/line/api/fj/fj_dist2fj.h
	Conversion of a LINE MAP into the arrival or service descriptor of the fork-join response-time-tail algorithm of Qiu, Perez and Harrison (IFIP Performance 2015).
file	include/line/api/fj/fj_gk_bound.h
	G(K) factors for the standardized-maximum approximation X_K^max ~ mu + sigma G(K).
file	include/line/api/fj/fj_harmonic.h
	Harmonic number H_K = sum_{k=1..K} 1/k.
file	include/line/api/fj/fj_ism_green.h
	Green's independent server model of simultaneous server requests.
file	include/line/api/fj/fj_lst_max_het.h
	Laplace-Stieltjes transform of the maximum of heterogeneous exponentials.
file	include/line/api/fj/fj_mg1_respt_moments.h
	Mean and variance of the M/G/1 response time, as ForkTail inputs.
file	include/line/api/fj/fj_order_stat.h
	CDF and expected value of the k-th order statistic of K i.i.d.
file	include/line/api/fj/fj_ordstat_exp.h
	Mean of the k-th smallest of n independent EXPONENTIAL branch completion times, i.e.
file	include/line/api/fj/fj_qgb.h
	Geometric bound on the queue length of a fork-join subnetwork.
file	include/line/api/fj/fj_quantile.h
	Quantile of the maximum of K i.i.d.
file	include/line/api/fj/fj_quorum_moments.h
	Mean and variance of a k-of-n (quorum) join completion time, from the mean and variance of each branch.
file	include/line/api/fj/fj_respt_2way.h
	Exact mean response time of a 2-way fork-join system of M/M/1 branches.
file	include/line/api/fj/fj_respt_bulk.h
	Centralized splitting analysed as an M[K]/M/c bulk arrival system.
file	include/line/api/fj/fj_respt_closed.h
	Varki bound on the residence time of a closed fork-join subnetwork.
file	include/line/api/fj/fj_respt_nosplit.h
	Mean response time of the distributed no-splitting parallel system.
file	include/line/api/fj/fj_respt_nt.h
	Nelson-Tantawi approximation to the mean response time of a K-way fork-join system of M/M/1 branches.
file	include/line/api/fj/fj_respt_varki.h
	Varki approximation to the mean response time of a K-way fork-join system of M/M/1 branches.
file	include/line/api/fj/fj_respt_vm.h
	Varma-Makowski light-traffic interpolation for the mean response time of a K-way fork-join system of M/M/1 branches.
file	include/line/api/fj/fj_rmax.h
	Pessimistic (independence) fork-join response time: the expected maximum of K independent M/M/1 response times, each exponential with rate mu - lambda.
file	include/line/api/fj/fj_rmax_erlang.h
	Expected maximum of K M/E_k/1 branch response times.
file	include/line/api/fj/fj_rmax_evd.h
	Extreme-value approximation to the maximum of K branch response times, from their mean and standard deviation.
file	include/line/api/fj/fj_serialization.h
	Blocking probability and pseudoserver delay of serialization phases.
file	include/line/api/fj/fj_sm_tput.h
	Saturated (single-message) maximum throughput of a K-way fork-join system with exponential branch service.
file	include/line/api/fj/fj_synch_delay.h
	Mean synchronization delay of a 2-way fork-join system of M/M/1 branches, i.e.
file	include/line/api/fj/fj_tail_forktail.h
	ForkTail black-box tail-latency approximation for fork-join requests.
file	include/line/api/fj/fj_tail_ordstat.h
	Tail latency of a k-of-n (QUORUM) fork-join request.
file	include/line/api/fj/fj_tsm_capacity.h
	Saturation throughput of the team service model.
file	include/line/api/fj/fj_types.h
	Shared return types and arithmetic helpers for the templated fork-join port.
file	include/line/api/fj/fj_xmax_2.h
	Expected maximum of two independent, possibly unequal-rate exponentials.
file	include/line/api/fj/fj_xmax_approx.h
	Two-moment approximation to the expected maximum of K i.i.d.
file	include/line/api/fj/fj_xmax_coxian.h
	Expected maximum of K i.i.d.
file	include/line/api/fj/fj_xmax_emma.h
	EMMA (Extreme-value Maximum Moment Approximation) to the expected maximum of K i.i.d.
file	include/line/api/fj/fj_xmax_erlang.h
	Expected maximum of K i.i.d.
file	include/line/api/fj/fj_xmax_exp.h
	Expected maximum of K i.i.d.
file	include/line/api/fj/fj_xmax_het.h
	Exact moments of the maximum of heterogeneous exponentials.
file	include/line/api/fj/fj_xmax_hyperexp.h
	Expected maximum of K i.i.d.
file	include/line/api/fj/fj_xmax_hz.h
	Harrison-Zertal approximation of the maximum of i.i.d.
file	include/line/api/fj/fj_xmax_hz_het.h
	Harrison-Zertal approximation of the maximum of general variables.
file	include/line/api/fj/fj_xmax_moments_het.h
	Moments of the maximum of heterogeneous exponentials by recurrence.
file	include/line/api/fj/fj_xmax_normal.h
	Expected maximum and variance of K i.i.d.
file	include/line/api/fj/fj_xmax_pareto.h
	Expected maximum and characteristic maximum of K i.i.d.

Detailed Description

Response time of the K-way fork-join queue, order statistics and expected maxima for the common branch laws, tail latency, split-merge and serialization.