Algorithm layer

line/api – the numerical algorithms, one directory and one namespace per domain, mirroring matlab/src/api, jline.api and line_solver.api. More...

Collaboration diagram for Algorithm layer:

Topics
	Age of information (aoi)
	Mean, variance and peak age of information for FCFS and LCFS queues, and the MAP-to-PH conversion the age solvers consume.
	Caches (cache)
	Miss rates, hit probabilities and normalizing constants of list-based caches: exact recursion, fixed-point iteration, importance sampling, ray integration, the saddle-point method, mean value analysis and mean field.
	Decomposition-aggregation (da)
	Drivers that split an integrated cache-queueing model into an isolated cache and a queueing network, then iterate the two to a fixed point.
	Discrete-time product-form networks (dpfqn)
	Normalizing constants of a discrete-time closed cycle of Bernoulli servers.
	Discrete-time queueing systems (dqsys)
	Single queues on a slot lattice: the Bernoulli server, Geo/Geo/1 and the batch-arrival Geo^X/Geo/1.
	Flow-equivalent servers (fes)
	Replace a subnetwork by one load-dependent station whose rate table is the throughput of the subnetwork over the population lattice (Chandy, Herzog and Woo 1975).
	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.
	Inference (infer)
	Demand and parameter estimation from measurements: maximum likelihood, fluid likelihood, variational methods and the queue-length reconstruction they consume.
	Loss networks (lossn)
	Blocking probabilities of a Kelly loss network: the Erlang fixed point, the Manjunath-Sikdar residue, decision-diagram recursion and Monte Carlo.
	Layered queueing networks (lqn)
	Algorithms over the layered structure itself, as opposed to the per-layer networks the LN solver builds from it.
	Transform inversion (lti)
	Numerical inversion of a Laplace transform by the Euler, Talbot and Gaver-Stehfest methods.
	Matrix-analytic methods (mam)
	MAPs, marked MAPs, MMPPs and phase-type distributions: moments, transformations, superposition, fitting (KPC-Toolbox, M3A, BuTools), and the QBD machinery for the rate matrices R and G.
	MAP queueing networks (mapqn)
	Networks whose arrival or service processes are MAPs, solved by approximate MVA and by the quasi-reduced form.
	Markov chains (mc)
	CTMC and DTMC algorithms: state-space generation, stationary and transient distributions, uniformization, Krylov kernels, passage times, stochastic complementation and the memory pre-gate.
	Decision diagrams (mdd)
	Quasi-reduced ordered multi-valued decision diagrams, and the closed-network and loss-network solves that store their state space in one.
	Maximum entropy (me)
	Maximum-entropy solutions of open and closed multiclass queueing networks.
	Markov-modulated deterministic processes (mmdp)
	The MMDP used as the input process of a fluid queue.
	Moment conversions (moment)
	Conversions between the moment families of a random variable – raw, central, factorial, binomial, cumulant and survival – together with the triangular transform tables and the multivariate cases.
	Non-product-form networks (npfqn)
	Networks outside BCMP: blocking, traffic-variability decomposition, queue decomposition and Lyapunov bounds.
	Permanents (perm)
	Exact and approximate matrix permanents – Ryser, Sinkhorn, Bethe, saddle-point and sampling – for the normalizing constants that are sums of permanents.
	Product-form networks (pfqn)
	The largest domain: exact and approximate mean value analysis, normalizing constants (convolution, RECAL, CoMoM, method of moments, Monte Carlo, asymptotic expansions), load-dependent and order-independent stations, bounds, and exact sensitivities and higher moments.
	Polling systems (polling)
	Mean delay of exhaustive, gated and limited polling with switchover times.
	Single queueing systems (qsys)
	One station in isolation, from M/M/1 to MAP/G/1/K: exact results, two-moment approximations, bounds, robust queueing, diffusion and fluid limits, and the scheduling variants.
	Delayed-hit retrieval (retrieval)
	Caches whose misses are served by a retrieval system, so a request that arrives during a fetch is a delayed hit rather than a miss.
	Output analysis (sim)
	What a simulation run's samples support: steady-state quantile confidence intervals, randomness and normality tests, and the quantiles they use.
	NetworkStruct utilities (sn)
	Operations on the sn structure itself – property detection, chains and visits, state handling, validation and the result tables.
	Stochastic network calculus (snc)
	MGF arrival and service envelopes, min-plus convolution, and the backlog and delay violation probabilities they bound.
	Stochastic Petri nets (spn)
	Product-form and linear-programming bounds for stochastic Petri nets.
	Summation method (sum)
	The summation method (SUM) and its extension (ESUM) for closed networks, including non-product-form stations with general service times.
	Symbolic arithmetic (sym)
	The symbolic engine behind the exact-arithmetic solvers, including the SymEngine and line-sage-rest backends.
	Trace analysis (trace)
	Statistics of a measured trace – moments, autocorrelation, indices of dispersion, binning and counting processes – for single and marked traces.
	Workflow analysis (wf)
	Detection and collapse of workflow patterns, and the complexity measures reported for them.

Detailed Description

line/api – the numerical algorithms, one directory and one namespace per domain, mirroring matlab/src/api, jline.api and line_solver.api.

Every routine is templated on the number type, so the same source runs in IEEE double, in exact rationals, or in fixed high-precision binary floating point.