Stochastic Network Utilities

Network analysis and transformation utilities.

The sn module contains utility functions for stochastic networks, including routing probability calculations, visit ratios, and network transformations.

Key function categories:

Network properties: sn_has_product_form(), sn_has_class_switching(), sn_has_fork_join()
Scheduling queries: sn_has_fcfs(), sn_has_ps(), sn_has_lcfs(), sn_has_priorities()
Model type queries: sn_is_open_model(), sn_is_closed_model(), sn_is_mixed_model()
Performance metrics: sn_get_demands_chain(), sn_get_arvr_from_tput(), sn_get_residt_from_respt()
State management: sn_get_state_aggr(), sn_is_state_valid(), sn_deaggregate_chain_results()
Routing utilities: sn_refresh_visits(), sn_rtnodes_to_rtorig(), sn_print_routing_matrix()

Service Network (SN) utilities.

Native Python implementations for stochastic network structure analysis, validation, and parameter extraction.

Key classes:: NetworkStruct: Data structure summarizing network characteristics SnGetDemandsResult: Result of sn_get_demands_chain calculation
Key functions:: sn_get_demands_chain: Aggregate class-level parameters into chain-level sn_has_*: Network property predicates sn_is_*: Model type checks sn_get_*: Parameter extraction sn_validate: Network validation

class MatrixArray(input_array)[source]

Bases: ndarray

Numpy array subclass with .get() and .set() methods for API compatibility.

This class provides compatibility with the wrapper mode that uses JLine’s Matrix class which has get(i, j) and set(i, j, value) methods.

Create MatrixArray from existing array.

__array_finalize__(obj)[source]: Handle view casting and new-from-template.

__getitem__(key)[source]

Override indexing to handle 2D indexing on 1D arrays.

This provides compatibility with MATLAB-style row/column vectors where a 1D array can be indexed as (0, j) or (i, 0).

static __new__(cls, input_array)[source]: Create MatrixArray from existing array.

__setitem__(key, value)[source]: Override item setting to handle 2D indexing on 1D arrays.

get(i, j=None)[source]

Get element at index (i, j) or just i if 1D.

Parameters:

i – Row index (or element index for 1D)
j – Column index (optional, for 2D arrays)

Returns:

Element value at the specified index

set(i, j, value=None)[source]

Set element at index (i, j) or just i if 1D.

Parameters:

i – Row index (or element index for 1D)
j – Column index or value (for 1D arrays)
value – Value to set (optional, for 2D arrays)

class NetworkStruct(nstations=0, nstateful=0, nnodes=0, nclasses=0, nchains=0, nclosedjobs=0, njobs=<factory>, nservers=<factory>, cap=None, classcap=None, rates=<factory>, scv=<factory>, phases=None, phasessz=None, phaseshift=None, visits=<factory>, nodevisits=<factory>, inchain=<factory>, chains=<factory>, refstat=<factory>, refclass=<factory>, sched=<factory>, schedparam=None, routing=<factory>, rt=None, rtnodes=None, nodetype=<factory>, isstation=<factory>, isstateful=<factory>, isstatedep=None, nodeToStation=<factory>, nodeToStateful=<factory>, stationToNode=<factory>, stationToStateful=<factory>, statefulToNode=<factory>, statefulToStation=<factory>, state=<factory>, stateprior=<factory>, space=<factory>, lldscaling=None, cdscaling=None, classprio=None, classdeadline=None, isslc=None, issignal=None, signaltype=None, syncreply=None, connmatrix=None, nodenames=<factory>, classnames=<factory>, mu=None, phi=None, proc=None, pie=None, procid=None, lst=None, fj=None, droprule=None, nregions=0, region=None, regionrule=None, regionweight=None, regionsz=None, sync=None, gsync=None, nodeparam=None, reward=None, rtorig=None, csmask=None, nvars=None)[source]

Bases: object

Data structure summarizing network characteristics.

This class is the Python equivalent in native Python. It contains all parameters needed by solvers to analyze a queueing network.

nstations

Number of stations (queues, delays, sources, joins, places)

Type:: int

nstateful

Number of stateful nodes

Type:: int

nnodes

Total number of nodes

Type:: int

nclasses

Number of job classes

Type:: int

nchains

Number of chains (routing chains)

Type:: int

nclosedjobs

Total number of jobs in closed classes

Type:: int

njobs

(1, K) Population per class (inf for open classes)

Type:: numpy.ndarray

nservers

(M, 1) Number of servers per station

Type:: numpy.ndarray

rates

(M, K) Service rates

Type:: numpy.ndarray

scv

(M, K) Squared coefficient of variation

Type:: numpy.ndarray

visits

Dict[int, ndarray] - Chain ID -> (M, K) visit ratios

Type:: Dict[int, numpy.ndarray]

inchain

Dict[int, ndarray] - Chain ID -> class indices in chain

Type:: Dict[int, numpy.ndarray]

chains

(K, 1) Chain membership per class

Type:: numpy.ndarray

refstat

(K, 1) Reference station per class

Type:: numpy.ndarray

refclass

(1, C) Reference class per chain

Type:: numpy.ndarray

sched

Dict[int, SchedStrategy] - Station ID -> scheduling strategy

Type:: Dict[int, int]

routing

(N, K) Routing strategy matrix

Type:: numpy.ndarray

rt

Routing probability matrix

Type:: numpy.ndarray | None

nodetype

List[NodeType] - Node types

Type:: List[int]

isstation

(N, 1) Boolean mask for stations

Type:: numpy.ndarray

isstateful

(N, 1) Boolean mask for stateful nodes

Type:: numpy.ndarray

nodeToStation

(N, 1) Node index -> station index mapping

Type:: numpy.ndarray

nodeToStateful

(N, 1) Node index -> stateful index mapping

Type:: numpy.ndarray

stationToNode

(M, 1) Station index -> node index mapping

Type:: numpy.ndarray

stationToStateful

(M, 1) Station index -> stateful index mapping

Type:: numpy.ndarray

statefulToNode

(S, 1) Stateful index -> node index mapping

Type:: numpy.ndarray

statefulToStation

(S, 1) Stateful index -> station index mapping

Type:: numpy.ndarray

state

Dict State per stateful node

Type:: Dict[int, numpy.ndarray]

lldscaling

(M, Nmax) Load-dependent scaling matrix

Type:: numpy.ndarray | None

cdscaling

Class-dependent scaling functions

Type:: Dict | None

cap

(M, 1) Station capacities

Type:: numpy.ndarray | None

classcap

(M, K) Per-class capacities

Type:: numpy.ndarray | None

connmatrix

(N, N) Connection matrix

Type:: numpy.ndarray | None

nodenames

List[str] - Node names

Type:: List[str]

classnames

List[str] - Class names

Type:: List[str]

__post_init__()[source]: Ensure arrays are MatrixArray (numpy arrays with .get()/.set() methods).

__repr__()[source]

String representation.

__setattr__(name, value)[source]

Override to convert numpy arrays to MatrixArray for API compatibility.

cap: numpy.ndarray | None = None

cdscaling: Dict | None = None

classcap: numpy.ndarray | None = None

classdeadline: numpy.ndarray | None = None

classprio: numpy.ndarray | None = None

connmatrix: numpy.ndarray | None = None

copy()[source]

Create a deep copy of this NetworkStruct.

csmask: numpy.ndarray | None = None

droprule: Dict | None = None

fj: numpy.ndarray | None = None

get_chain_population(chain_id)[source]

Get total population in a chain.

Parameters:: chain_id (int) – Chain index (0-based)
Returns:: Total number of jobs in the chain
Return type:: float

get_closed_class_indices()[source]

Get indices of closed classes.

get_open_class_indices()[source]

Get indices of open classes.

get_scheduling_at_station(station_id)[source]

Get scheduling strategy at a station.

Parameters:: station_id (int) – Station index (0-based)
Returns:: SchedStrategy value
Return type:: int

get_stateful_indices()[source]

Get indices of stateful nodes.

Returns:: Array of node indices that are stateful
Return type:: numpy.ndarray

get_station_indices()[source]

Get indices of station nodes.

Returns:: Array of node indices that are stations
Return type:: numpy.ndarray

get_total_population()[source]

Get total population across all closed classes.

gsync: Dict | None = None

has_class_dependence()[source]

Check if model has class-dependent scaling.

has_closed_classes()[source]

Check if model has closed (finite population) classes.

has_load_dependence()[source]

Check if model has load-dependent service rates.

has_multi_server()[source]

Check if any station has multiple servers.

has_open_classes()[source]

Check if model has open (infinite population) classes.

is_closed_chain(chain_id)[source]

Check if a chain is closed (finite population).

Parameters:: chain_id (int) – Chain index (0-based)
Returns:: True if chain is closed, False if open
Return type:: bool

is_open_chain(chain_id)[source]

Check if a chain is open (infinite population).

Parameters:: chain_id (int) – Chain index (0-based)
Returns:: True if chain is open, False if closed
Return type:: bool

is_valid()[source]

Check if structure is valid.

Returns:: True if structure passes validation, False otherwise
Return type:: bool

issignal: numpy.ndarray | None = None

isslc: numpy.ndarray | None = None

isstatedep: numpy.ndarray | None = None

lldscaling: numpy.ndarray | None = None

lst: Dict | None = None

mu: Dict | None = None

nchains: int = 0

nclasses: int = 0

nclosedjobs: int = 0

nnodes: int = 0

nodeparam: Dict | None = None

nregions: int = 0

nstateful: int = 0

nstations: int = 0

nvars: numpy.ndarray | None = None

property obj: Return self for compatibility with wrapper code that accesses .obj

phases: numpy.ndarray | None = None

phaseshift: numpy.ndarray | None = None

phasessz: numpy.ndarray | None = None

phi: Dict | None = None

pie: Dict | None = None

proc: Dict | None = None

procid: Dict | None = None

region: List | None = None

regionrule: numpy.ndarray | None = None

regionsz: numpy.ndarray | None = None

regionweight: numpy.ndarray | None = None

reward: Dict | None = None

rt: numpy.ndarray | None = None

rtnodes: numpy.ndarray | None = None

rtorig: Dict | None = None

schedparam: numpy.ndarray | None = None

signaltype: List | None = None

sync: Dict | None = None

syncreply: numpy.ndarray | None = None

validate()[source]

Validate structural consistency.

Raises:: ValueError – If structural consistency is violated

njobs: numpy.ndarray

nservers: numpy.ndarray

rates: numpy.ndarray

scv: numpy.ndarray

visits: Dict[int, numpy.ndarray]

nodevisits: Dict[int, numpy.ndarray]

inchain: Dict[int, numpy.ndarray]

chains: numpy.ndarray

refstat: numpy.ndarray

refclass: numpy.ndarray

sched: Dict[int, int]

routing: numpy.ndarray

nodetype: List[int]

isstation: numpy.ndarray

isstateful: numpy.ndarray

nodeToStation: numpy.ndarray

nodeToStateful: numpy.ndarray

stationToNode: numpy.ndarray

stationToStateful: numpy.ndarray

statefulToNode: numpy.ndarray

statefulToStation: numpy.ndarray

state: Dict[int, numpy.ndarray]

stateprior: Dict[int, numpy.ndarray]

space: Dict[int, numpy.ndarray]

nodenames: List[str]

classnames: List[str]

class NodeType(*values)[source]

Bases: IntEnum

Node types in a queueing network.

NOTE: Values must match lang/base.py NodeType enum.

static toText(node_type)[source]

Convert node type to text representation.

SOURCE = 0

SINK = 1

QUEUE = 2

DELAY = 3

JOIN = 5

CACHE = 6

ROUTER = 7

CLASSSWITCH = 8

PLACE = 9

TRANSITION = 10

LOGGER = 11

FINITE_CAPACITY_REGION = 12

class SchedStrategy(*values)[source]

Bases: IntEnum

Scheduling strategies.

LCFSPI = 3

HOL = 9

LPS = 17

SETF = 18

class RoutingStrategy(*values)[source]

Bases: IntEnum

Routing strategies.

RL = 6

CLASS_SWITCH = 8

class DropStrategy(*values)[source]

Bases: IntEnum

Drop strategies for finite capacity.

WAITQ = 0

DROP = 1

BAS = 2

sn_get_demands_chain(sn)[source]

Calculate new queueing network parameters after aggregating classes into chains.

This function computes chain-level demands, service times, visit ratios, and other parameters by aggregating class-level data based on chain membership.

Parameters:

sn (NetworkStruct) – NetworkStruct object for the queueing network model

Returns:

Lchain: (M, C) chain-level demand matrix
STchain: (M, C) chain-level service time matrix
Vchain: (M, C) chain-level visit ratio matrix
alpha: (M, K) class-to-chain weighting matrix
Nchain: (1, C) population per chain
SCVchain: (M, C) chain-level squared coefficient of variation
refstatchain: (C, 1) reference station per chain

Return type:

SnGetDemandsResult containing chain parameters

class SnGetDemandsResult(Lchain, STchain, Vchain, alpha, Nchain, SCVchain, refstatchain)[source]

Bases: object

Result of sn_get_demands_chain calculation.

Lchain

(M, C) Chain-level demand matrix

Type:: numpy.ndarray

STchain

(M, C) Chain-level service time matrix

Type:: numpy.ndarray

Vchain

(M, C) Chain-level visit ratio matrix

Type:: numpy.ndarray

alpha

(M, K) Class-to-chain weighting matrix

Type:: numpy.ndarray

Nchain

(1, C) Population per chain

Type:: numpy.ndarray

SCVchain

(M, C) Chain-level squared coefficient of variation

Type:: numpy.ndarray

refstatchain

(C, 1) Reference station per chain

Type:: numpy.ndarray

Lchain: numpy.ndarray

STchain: numpy.ndarray

Vchain: numpy.ndarray

alpha: numpy.ndarray

Nchain: numpy.ndarray

SCVchain: numpy.ndarray

refstatchain: numpy.ndarray

sn_deaggregate_chain_results(sn, Lchain, ST, STchain, Vchain, alpha, Qchain, Uchain, Rchain, Tchain, Cchain, Xchain)[source]

Calculate class-based performance metrics from chain-level performance measures.

This function disaggregates chain-level performance metrics (queue lengths, utilizations, response times, throughputs) to class-level metrics using the aggregation factors (alpha).

Parameters:

sn (NetworkStruct) – NetworkStruct object for the queueing network model
Lchain (numpy.ndarray) – (M, C) Service demands per chain
ST (numpy.ndarray | None) – (M, K) Mean service times per class (optional, computed from rates if None)
STchain (numpy.ndarray) – (M, C) Mean service times per chain
Vchain (numpy.ndarray) – (M, C) Mean visits per chain
alpha (numpy.ndarray) – (M, K) Class aggregation coefficients
Qchain (numpy.ndarray | None) – (M, C) Mean queue-lengths per chain (optional)
Uchain (numpy.ndarray | None) – (M, C) Mean utilization per chain (optional)
Rchain (numpy.ndarray) – (M, C) Mean response time per chain
Tchain (numpy.ndarray) – (M, C) Mean throughput per chain
Cchain (numpy.ndarray | None) – (1, C) Mean system response time per chain (optional, not yet supported)
Xchain (numpy.ndarray) – (1, C) Mean system throughput per chain

Returns:

Q: (M, K) queue lengths
U: (M, K) utilizations
R: (M, K) response times
T: (M, K) throughputs
C: (1, K) system response times
X: (1, K) system throughputs

Return type:

SnDeaggregateResult containing class-level performance metrics

Raises:

RuntimeError – If Cchain is provided (not yet supported)

class SnDeaggregateResult(Q, U, R, T, C, X)[source]

Bases: object

Result of sn_deaggregate_chain_results calculation.

Q

(M, K) Class-level queue lengths

Type:: numpy.ndarray

U

(M, K) Class-level utilizations

Type:: numpy.ndarray

R

(M, K) Class-level response times

Type:: numpy.ndarray

T

(M, K) Class-level throughputs

Type:: numpy.ndarray

C

(1, K) Class-level system response times

Type:: numpy.ndarray

X

(1, K) Class-level system throughputs

Type:: numpy.ndarray

Q: numpy.ndarray

U: numpy.ndarray

R: numpy.ndarray

T: numpy.ndarray

C: numpy.ndarray

X: numpy.ndarray

class ProductFormParams(lam, D, N, Z, mu, S, V)[source]

Bases: NamedTuple

Result of sn_get_product_form_params calculation.

Create new instance of ProductFormParams(lam, D, N, Z, mu, S, V)

D: numpy.ndarray: Alias for field number 1

N: numpy.ndarray: Alias for field number 2

S: numpy.ndarray: Alias for field number 5

V: numpy.ndarray: Alias for field number 6

Z: numpy.ndarray: Alias for field number 3

lam: numpy.ndarray: Alias for field number 0

mu: numpy.ndarray: Alias for field number 4

sn_get_product_form_params(sn)[source]

Extract standard product-form parameters from the network structure.

This function extracts class-level parameters from a network structure for use in product-form queueing network analysis.

Parameters:

sn (NetworkStruct) – NetworkStruct object

Returns:

lam: Arrival rates for open classes
D: Service demands at queueing stations
N: Population vector
Z: Think times (service demands at delay stations)
mu: Load-dependent service capacity scaling factors
S: Number of servers at queueing stations
V: Visit ratios

Return type:

ProductFormParams containing

References

MATLAB: matlab/src/api/sn/sn_get_product_form_params.m

sn_get_residt_from_respt(sn, RN, WH=None)[source]

Compute residence times from response times.

This function converts response times to residence times by accounting for visit ratios at each station.

Parameters:

sn (NetworkStruct) – NetworkStruct object
RN (numpy.ndarray) – Average response times (M, K)
WH (Dict | None) – Residence time handles (optional)

Returns:

Average residence times (M, K)

Return type:

WN

References

MATLAB: matlab/src/api/sn/sn_get_residt_from_respt.m

sn_get_state_aggr(sn)[source]

Get aggregated state representation.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: Dictionary mapping stateful node index to aggregated state
Return type:: Dict[int, numpy.ndarray]

References

MATLAB: matlab/src/api/sn/sn_get_state_aggr.m

sn_set_arrival(sn, station_idx, class_idx, rate)[source]

Set arrival rate for a class at a station.

Parameters:

sn (NetworkStruct) – NetworkStruct object (modified in place)
station_idx (int) – Station index (0-based)
class_idx (int) – Class index (0-based)
rate (float) – Arrival rate

References

MATLAB: matlab/src/api/sn/sn_set_arrival.m

sn_set_service(sn, station_idx, class_idx, rate, scv=1.0)[source]

Set service rate for a class at a station.

Parameters:

sn (NetworkStruct) – NetworkStruct object (modified in place)
station_idx (int) – Station index (0-based)
class_idx (int) – Class index (0-based)
rate (float) – Service rate
scv (float) – Squared coefficient of variation (default 1.0 for exponential)

References

MATLAB: matlab/src/api/sn/sn_set_service.m

sn_set_servers(sn, station_idx, nservers)[source]

Set number of servers at a station.

Parameters:

sn (NetworkStruct) – NetworkStruct object (modified in place)
station_idx (int) – Station index (0-based)
nservers (int) – Number of servers

References

MATLAB: matlab/src/api/sn/sn_set_servers.m

sn_set_population(sn, class_idx, njobs)[source]

Set population for a class.

Parameters:

sn (NetworkStruct) – NetworkStruct object (modified in place)
class_idx (int) – Class index (0-based)
njobs (float) – Number of jobs (inf for open class)

References

MATLAB: matlab/src/api/sn/sn_set_population.m

sn_set_priority(sn, class_idx, priority)[source]

Set priority for a class.

Parameters:

sn (NetworkStruct) – NetworkStruct object (modified in place)
class_idx (int) – Class index (0-based)
priority (int) – Priority level (higher = more priority)

References

MATLAB: matlab/src/api/sn/sn_set_priority.m

sn_set_routing(sn, source_node, dest_node, source_class, dest_class, prob)[source]

Set routing probability between nodes and classes.

Parameters:

sn (NetworkStruct) – NetworkStruct object (modified in place)
source_node (int) – Source node index (0-based)
dest_node (int) – Destination node index (0-based)
source_class (int) – Source class index (0-based)
dest_class (int) – Destination class index (0-based)
prob (float) – Routing probability

References

MATLAB: matlab/src/api/sn/sn_set_routing.m

sn_refresh_visits(sn)[source]

Refresh visit ratios from routing matrix.

This function solves traffic equations to compute visit ratios at each station from the routing probability matrix.

Parameters:: sn (NetworkStruct) – NetworkStruct object (modified in place)

References

MATLAB: matlab/src/api/sn/sn_refresh_visits.m

sn_set_fork_fanout(sn, fork_node_idx, fan_out)[source]

Set fork fanout (tasksPerLink) for a Fork node.

Updates the fanOut field in nodeparam for a Fork node.

Parameters:

sn (NetworkStruct) – NetworkStruct object
fork_node_idx (int) – Node index of the Fork node (0-based)
fan_out (int) – Number of tasks per output link (>= 1)

Returns:

Modified NetworkStruct

Raises:

ValueError – If the specified node is not a Fork node

Return type:

NetworkStruct

References

MATLAB: matlab/src/api/sn/sn_set_fork_fanout.m

sn_set_service_batch(sn, rates, scvs=None, auto_refresh=False)[source]

Set service rates for multiple station-class pairs.

Batch update of service rates. NaN values are skipped (not updated). More efficient than calling sn_set_service multiple times.

Parameters:

sn (NetworkStruct) – NetworkStruct object
rates (numpy.ndarray) – Matrix of new rates (nstations x nclasses), NaN = skip
scvs (numpy.ndarray | None) – Matrix of new SCVs (optional)
auto_refresh (bool) – If True, refresh process fields (default False)

Returns:

Modified NetworkStruct

Return type:

NetworkStruct

References

MATLAB: matlab/src/api/sn/sn_set_service_batch.m

sn_nonmarkov_toph(sn, options=None)[source]

Convert non-Markovian distributions to Phase-Type using approximation.

This function scans all service and arrival processes in the network structure and converts non-Markovian distributions to Markovian Arrival Processes (MAPs) using the specified approximation method.

Supported non-Markovian distributions: - GAMMA: Gamma distribution - WEIBULL: Weibull distribution - LOGNORMAL: Lognormal distribution - PARETO: Pareto distribution - UNIFORM: Uniform distribution - DET: Deterministic (converted to Erlang)

Parameters:

sn (NetworkStruct) – NetworkStruct object (from getStruct())
options (Dict[str, Any] | None) – Solver options dict with fields: - config.nonmkv: Method for conversion (‘none’, ‘bernstein’) - config.nonmkvorder: Number of phases for approximation (default 20) - config.preserveDet: Keep deterministic distributions (for MAP/D/c)

Returns:

Modified NetworkStruct with converted processes

Return type:

NetworkStruct

References

MATLAB: matlab/src/api/sn/sn_nonmarkov_toph.m

class ChainParams(lambda_vec, D, N, Z, mu, S, V)[source]

Bases: object

Chain-aggregated product-form parameters.

lambda_vec: numpy.ndarray

D: numpy.ndarray

N: numpy.ndarray

Z: numpy.ndarray

mu: numpy.ndarray

S: numpy.ndarray

V: numpy.ndarray

sn_get_arvr_from_tput(sn, TN, TH=None)[source]

Compute average arrival rates at stations from throughputs.

Calculates the average arrival rate at each station in steady-state from the station throughputs and routing matrix.

Parameters:

sn (NetworkStruct) – Network structure
TN (numpy.ndarray) – Average throughputs at stations (M x R)
TH (numpy.ndarray | None) – Throughput handles (optional)

Returns:

Average arrival rates at stations (M x R)

Return type:

AN

References

Original MATLAB: matlab/src/api/sn/sn_get_arvr_from_tput.m

sn_get_node_arvr_from_tput(sn, TN, TH=None, AN=None)[source]

Compute node arrival rates from station throughputs.

This function handles: - Station nodes: Uses station arrival rates directly - Cache nodes: Only requesting classes arrive (not hit/miss classes) - Non-station nodes (ClassSwitch, Sink): Uses nodevisits-based computation

Parameters:

sn (NetworkStruct) – Network structure
TN (numpy.ndarray) – Station throughputs (M x R)
TH (numpy.ndarray | None) – Throughput handles (optional)
AN (numpy.ndarray | None) – Station arrival rates (optional, computed if not provided)

Returns:

Node arrival rates (I x R)

Return type:

ANn

References

Original MATLAB: matlab/src/api/sn/sn_get_node_arvr_from_tput.m

sn_get_node_tput_from_tput(sn, TN, TH=None, ANn=None)[source]

Compute node throughputs from station throughputs.

This function handles: - Station nodes: Uses station throughputs directly - Cache nodes: Uses actual hit/miss probabilities if available - Non-station nodes: Uses routing matrix (rtnodes) for computation

Parameters:

sn (NetworkStruct) – Network structure
TN (numpy.ndarray) – Station throughputs (M x R)
TH (numpy.ndarray | None) – Throughput handles (optional)
ANn (numpy.ndarray | None) – Node arrival rates (optional, computed if not provided)

Returns:

Node throughputs (I x R)

Return type:

TNn

References

Original MATLAB: matlab/src/api/sn/sn_get_node_tput_from_tput.m

sn_get_product_form_chain_params(sn)[source]

Extract product-form parameters aggregated by chain.

Extracts parameters from a network structure and aggregates them by chain for use in product-form analysis methods.

Parameters:: sn (NetworkStruct) – Network structure
Returns:: ChainParams with lambda_vec, D, N, Z, mu, S, V
Return type:: ChainParams

References

Original MATLAB: matlab/src/api/sn/sn_get_product_form_chain_params.m

sn_set_routing_prob(sn, from_stateful, from_class, to_stateful, to_class, prob, auto_refresh=False)[source]

Set a routing probability between two stateful node-class pairs.

Updates a single entry in the rt matrix.

Parameters:

sn (NetworkStruct) – Network structure
from_stateful (int) – Source stateful node index (0-based)
from_class (int) – Source class index (0-based)
to_stateful (int) – Destination stateful node index (0-based)
to_class (int) – Destination class index (0-based)
prob (float) – Routing probability [0, 1]
auto_refresh (bool) – If True, refresh visit ratios (default False)

Returns:

Modified network structure

Return type:

NetworkStruct

References

Original MATLAB: matlab/src/api/sn/sn_set_routing_prob.m

sn_is_closed_model(sn)[source]

Check if the network model is closed (all finite populations).

A closed model has finite jobs and no infinite (open) job classes.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if the network is a closed model
Return type:: bool

sn_is_open_model(sn)[source]

Check if the network model is open (all infinite populations).

An open model has only infinite (open) job classes.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if the network is an open model
Return type:: bool

sn_is_mixed_model(sn)[source]

Check if the network model is mixed (both open and closed classes).

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if the network has both open and closed classes
Return type:: bool

sn_is_population_model(sn)[source]

Check if the network model has populations defined.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if population is defined
Return type:: bool

sn_has_closed_classes(sn)[source]

Check if the network has closed (finite population) classes.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one closed class
Return type:: bool

sn_has_open_classes(sn)[source]

Check if the network has open (infinite population) classes.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one open class
Return type:: bool

sn_has_mixed_classes(sn)[source]

Check if the network has both open and closed classes.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has both open and closed classes
Return type:: bool

sn_has_single_class(sn)[source]

Check if the network has exactly one class.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has exactly one class
Return type:: bool

sn_has_multi_class(sn)[source]

Check if the network has multiple classes.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has more than one class
Return type:: bool

sn_has_multiple_closed_classes(sn)[source]

Check if the network has multiple closed classes.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has more than one closed class
Return type:: bool

sn_has_single_chain(sn)[source]

Check if the network has exactly one chain.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has exactly one chain
Return type:: bool

sn_has_multi_chain(sn)[source]

Check if the network has multiple chains.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has more than one chain
Return type:: bool

sn_has_fcfs(sn)[source]

Check if the network has any FCFS (First-Come First-Served) stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one FCFS station
Return type:: bool

sn_has_ps(sn)[source]

Check if the network has any PS (Processor Sharing) stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one PS station
Return type:: bool

sn_has_inf(sn)[source]

Check if the network has any INF (Infinite Server/Delay) stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one INF station
Return type:: bool

sn_has_lcfs(sn)[source]

Check if the network has any LCFS (Last-Come First-Served) stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one LCFS station
Return type:: bool

sn_has_lcfspr(sn)[source]

Check if the network has any LCFS-PR (LCFS Preemptive Resume) stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one LCFS-PR station
Return type:: bool

sn_has_lcfs_pi(sn)[source]

Check if the network has any LCFS-PI (LCFS Preemptive Identical) stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one LCFS-PI station
Return type:: bool

sn_has_siro(sn)[source]

Check if the network has any SIRO (Service In Random Order) stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one SIRO station
Return type:: bool

sn_has_dps(sn)[source]

Check if the network has any DPS (Discriminatory Processor Sharing) stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one DPS station
Return type:: bool

sn_has_dps_prio(sn)[source]

Check if the network has any DPS with priority stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one DPS-PRIO station
Return type:: bool

sn_has_gps(sn)[source]

Check if the network has any GPS (Generalized Processor Sharing) stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one GPS station
Return type:: bool

sn_has_gps_prio(sn)[source]

Check if the network has any GPS with priority stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one GPS-PRIO station
Return type:: bool

sn_has_ps_prio(sn)[source]

Check if the network has any PS with priority stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one PS-PRIO station
Return type:: bool

sn_has_hol(sn)[source]

Check if the network has any HOL (Head of Line) priority stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one HOL station
Return type:: bool

sn_has_lps(sn)[source]

Check if the network has any LPS (Least Progress Scheduling) stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one LPS station
Return type:: bool

sn_has_setf(sn)[source]

Check if the network has any SETF (Shortest Elapsed Time First) stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one SETF station
Return type:: bool

sn_has_sept(sn)[source]

Check if the network has any SEPT (Shortest Expected Processing Time) stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one SEPT station
Return type:: bool

sn_has_lept(sn)[source]

Check if the network has any LEPT (Longest Expected Processing Time) stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one LEPT station
Return type:: bool

sn_has_sjf(sn)[source]

Check if the network has any SJF (Shortest Job First) stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one SJF station
Return type:: bool

sn_has_ljf(sn)[source]

Check if the network has any LJF (Longest Job First) stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one LJF station
Return type:: bool

sn_has_polling(sn)[source]

Check if the network has any polling stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has at least one polling station
Return type:: bool

sn_has_homogeneous_scheduling(sn, strategy)[source]

Check if the network uses an identical scheduling strategy at every station.

Parameters:

sn (NetworkStruct) – NetworkStruct object
strategy (int) – SchedStrategy value to check for

Returns:

True if all stations use the specified strategy

Return type:

bool

sn_has_multi_class_fcfs(sn)[source]

Check if the network has a multiclass FCFS station.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has multiclass and at least one FCFS station
Return type:: bool

sn_has_multi_class_heter_fcfs(sn)[source]

Check if network has multiclass heterogeneous FCFS stations.

A heterogeneous FCFS station has different service rates for different classes.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has FCFS stations with heterogeneous class rates
Return type:: bool

sn_has_multi_class_heter_exp_fcfs(sn)[source]

Check if network has multiclass heterogeneous exponential FCFS stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has FCFS stations with heterogeneous exponential service
Return type:: bool

sn_has_multi_server(sn)[source]

Check if the network has any multi-server stations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if any station has more than one server
Return type:: bool

sn_has_load_dependence(sn)[source]

Check if the network has load-dependent service.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has load-dependent scaling
Return type:: bool

sn_has_joint_dependence(sn)[source]

Check if the network has joint-dependent service rates.

This includes both LJD (Limited Joint Dependence) and LJCD (Limited Joint Class Dependence) scaling.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has joint-dependent scaling
Return type:: bool

sn_has_fork_join(sn)[source]

Check if the network uses fork and/or join nodes.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has fork-join topology
Return type:: bool

sn_has_priorities(sn)[source]

Check if the network uses class priorities.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if the network has priority-based scheduling (non-uniform priorities)
Return type:: bool

sn_has_class_switching(sn)[source]

Check if the network has class switching.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has class switching
Return type:: bool

sn_has_fractional_populations(sn)[source]

Check if the network has fractional (non-integer) populations.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if any class has fractional population
Return type:: bool

sn_has_sd_routing(sn)[source]

Check if the network has state-dependent routing strategies.

State-dependent routing strategies violate the product-form assumption. These include Round-Robin, Weighted Round-Robin, Join Shortest Queue, Power of K Choices, and Reinforcement Learning.

Product-form requires state-independent (Markovian) routing. PROB and RAND are product-form compatible.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has state-dependent routing
Return type:: bool

sn_has_product_form(sn)[source]

Check if the network has a known product-form solution.

A network has product form if: - All stations use INF, PS, FCFS, LCFS-PR, or EXT scheduling - No multiclass heterogeneous FCFS - No priorities - No fork-join

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network has product-form solution
Return type:: bool

sn_has_product_form_not_het_fcfs(sn)[source]

Check if network has product form except for heterogeneous FCFS.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network would have product form without heterogeneous FCFS
Return type:: bool

sn_has_product_form_except_multi_class_heter_exp_fcfs(sn)[source]

Check if network has product form except for multiclass heterogeneous exponential FCFS.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if network would have product form without multiclass heter exp FCFS
Return type:: bool

sn_is_state_valid(sn)[source]

Check if the network state is valid.

Parameters:: sn (NetworkStruct) – NetworkStruct object
Returns:: True if state is valid
Return type:: bool

sn_print(sn, file=None)[source]

Print comprehensive information about a NetworkStruct object.

This function displays all fields, matrices, lists, and maps in a formatted manner useful for debugging and inspection of network structures.

Parameters:

sn (NetworkStruct) – Network structure to inspect
file – Output file (default: sys.stdout)

References

MATLAB: matlab/src/api/sn/sn_print.m

sn_print_routing_matrix(sn, onlyclass=None, file=None)[source]

Print the routing matrix of the network.

This function displays the routing probabilities between nodes and classes in a human-readable format.

Parameters:

sn (NetworkStruct) – Network structure
onlyclass (Any | None) – Optional filter for a specific class (object with ‘name’ attribute)
file – Output file (default: sys.stdout)

References

MATLAB: matlab/src/api/sn/sn_print_routing_matrix.m

sn_refresh_process_fields(sn, station_idx, class_idx)[source]

Refresh process fields based on rate and SCV values.

Updates mu, phi, proc, pie, phases based on current rate and SCV values. - SCV = 1.0: Exponential (1 phase) - SCV < 1.0: Erlang approximation - SCV > 1.0: Hyperexponential(2) approximation

Parameters:

sn (NetworkStruct) – Network structure (modified in place)
station_idx (int) – Station index (0-based)
class_idx (int) – Class index (0-based)

Returns:

Modified network structure

Return type:

NetworkStruct

References

MATLAB: matlab/src/api/sn/sn_refresh_process_fields.m

sn_rtnodes_to_rtorig(sn)[source]

Convert node routing matrix to the original routing matrix format.

This function converts the node-level routing matrix to the original routing matrix format, excluding class-switching nodes.

Parameters:: sn (NetworkStruct) – Network structure
Returns:: rtorigcell: Dictionary representation {(r,s): ndarray} rtorig: Sparse/dense matrix representation
Return type:: Tuple of (rtorigcell, rtorig) where

References

MATLAB: matlab/src/api/sn/sn_rtnodes_to_rtorig.m