Stochastic Network Utilities

Network analysis and transformation utilities.

Network analysis utilities for checking properties and computing derived metrics.

Function List

• sn_deaggregate_chain_results - Deaggregates chain-level performance metrics to class-level metrics
• sn_get_arvr_from_tput - Computes average arrival rates at stations from throughputs
• sn_get_demands_chain - Computes aggregated demand parameters per chain
• sn_get_node_arvr_from_tput - Computes average arrival rates at nodes from station throughputs
• sn_get_node_tput_from_tput - Computes average throughputs at nodes from station throughputs
• sn_get_product_form_chain_params - Extracts product-form parameters aggregated by chain
• sn_get_product_form_params - Extracts standard product-form parameters from the network structure
• sn_get_residt_from_respt - Computes residence times from response times
• sn_get_state_aggr - Returns the aggregated initial state of the network
• sn_has_class_switching - Checks if the network has class switching
• sn_has_closed_classes - Checks if the network contains closed classes
• sn_has_dps - Checks if the network uses Discriminatory Processor Sharing
• sn_has_dps_prio - Checks if the network uses DPS with priorities
• sn_has_fcfs - Checks if the network has FCFS scheduling
• sn_has_fork_join - Checks if the network contains fork-join nodes
• sn_has_fractional_populations - Checks if the network has fractional population values
• sn_has_gps - Checks if the network uses GPS scheduling
• sn_has_gps_prio - Checks if the network uses GPS with priorities
• sn_has_hol - Checks if the network uses HOL scheduling
• sn_has_homogeneous_scheduling - Checks if all stations use the same scheduling policy
• sn_has_inf - Checks if the network has infinite server stations
• sn_has_lcfs - Checks if the network uses LCFS scheduling
• sn_has_lcfs_pi - Checks if the network uses LCFS with preemptive-identical scheduling
• sn_has_lcfs_pr - Checks if the network uses LCFS with preemptive-resume scheduling
• sn_has_lept - Checks if the network uses LEPT scheduling
• sn_has_ljf - Checks if the network uses LJF scheduling
• sn_has_load_dependence - Checks if the network has load-dependent service rates
• sn_has_mixed_classes - Checks if the network has both open and closed classes
• sn_has_multi_chain - Checks if the network has multiple chains
• sn_has_multi_class_fcfs - Checks if the network has multi-class FCFS stations
• sn_has_multi_class_heter_exp_fcfs - Checks for multi-class FCFS with heterogeneous exponential service
• sn_has_multi_class_heter_fcfs - Checks for multi-class FCFS with heterogeneous service
• sn_has_multi_class - Checks if the network has multiple classes
• sn_has_multiple_closed_classes - Checks if the network has multiple closed classes
• sn_has_multi_server - Checks if the network has multi-server stations
• sn_has_open_classes - Checks if the network contains open classes
• sn_has_priorities - Checks if the network uses priority scheduling
• sn_has_product_form - Checks if the network has product-form solution
• sn_has_product_form_not_het_fcfs - Checks for product-form excluding heterogeneous FCFS
• sn_has_ps - Checks if the network uses PS scheduling
• sn_has_ps_prio - Checks if the network uses PS with priorities
• sn_has_sept - Checks if the network uses SEPT scheduling
• sn_has_single_chain - Checks if the network has a single chain
• sn_has_single_class - Checks if the network has a single class
• sn_has_siro - Checks if the network uses SIRO scheduling
• sn_has_sjf - Checks if the network uses SJF scheduling
• sn_is_closed_model - Checks if the network is a closed model
• sn_is_mixed_model - Checks if the network is a mixed model
• sn_is_open_model - Checks if the network is an open model
• sn_is_population_model - Checks if the network is defined by populations
• sn_is_state_valid - Validates a network state
• sn_print - Prints comprehensive information about a NetworkStruct object
• sn_print_routing_matrix - Prints the routing matrix of the network
• sn_refresh_visits - Solves traffic equations to compute visit ratios
• sn_rtnodes_to_rtorig - Converts node routing matrix to the original routing matrix format

sn_deaggregate_chain_results

Description: Deaggregates chain-level performance metrics to class-level metrics

Syntax:

[Q, U, R, T, C, X] = sn_deaggregate_chain_results(sn, Lchain, ST, STchain, Vchain, alpha, Qchain, Uchain, Rchain, Tchain, Cchain, Xchain)

Parameters:

Name	Description
sn	Stochastic network structure
Lchain	Service demand per chain
ST	Service time matrix
STchain	Service time per chain
Vchain	Visit ratios per chain
alpha	Initial probability vector or shape parameter
Qchain	Queue length per chain
Uchain	Utilization per chain
Rchain	Response time per chain
Tchain	Response time per chain
Cchain	Cycle time per chain
Xchain	Throughput per chain

Returns:

Name	Description
Q	Generator matrix or queue lengths
U	Utilization matrix
R	R matrix (QBD) or response times
T	Transient generator or service times
C	Coefficient matrix or cost
X	Throughput matrix

sn_get_arvr_from_tput

Description: Computes average arrival rates at stations from throughputs

Syntax:

sn_get_arvr_from_tput(...)

sn_get_demands_chain

Description: Computes aggregated demand parameters per chain

Syntax:

[Lchain, STchain, Vchain, alpha, Nchain, SCVchain, refstatchain] = sn_get_demands_chain(sn)

Parameters:

Name	Description
sn	Stochastic network structure

Returns:

Name	Description
Lchain	Service demand per chain
STchain	Service time per chain
Vchain	Visit ratios per chain
alpha	Initial probability vector (phase-type)
Nchain	Population per chain
SCVchain	Squared coefficient of variation per chain
refstatchain	Reference state per chain

sn_get_node_arvr_from_tput

Description: Computes average arrival rates at nodes from station throughputs

Syntax:

sn_get_node_arvr_from_tput(...)

sn_get_node_tput_from_tput

Description: Computes average throughputs at nodes from station throughputs

Syntax:

sn_get_node_tput_from_tput(...)

sn_get_product_form_chain_params

Description: Extracts product-form parameters aggregated by chain

Syntax:

[lambda, D, N, Z, mu, S, V] = sn_get_product_form_chain_params(sn)

Parameters:

Name	Description
sn	Stochastic network structure

Returns:

Name	Description
lambda	Arrival rates or eigenvalues
D	Service demand matrix
N	Population vector or number of classes
Z	Think times or partition function
mu	Service rates or mean values
S	Service time or state probabilities
V	Visit ratios

sn_get_product_form_params

Description: Extracts standard product-form parameters from the network structure

Syntax:

[lambda, D, N, Z, mu, S, V] = sn_get_product_form_params(sn)

Parameters:

Name	Description
sn	Stochastic network structure

Returns:

Name	Description
lambda	Arrival rates or eigenvalues
D	Service demand matrix
N	Population vector or number of classes
Z	Think times or partition function
mu	Service rates or mean values
S	Service time or state probabilities
V	Visit ratios

sn_get_residt_from_respt

Description: Computes residence times from response times

Syntax:

sn_get_residt_from_respt(...)

sn_get_state_aggr

Description: Returns the aggregated initial state of the network

Syntax:

initialStateAggr = sn_get_state_aggr(sn)

Parameters:

Name	Description
sn	Stochastic network structure

Returns:

Name	Description
initialStateAggr	Initial state after aggregation

sn_has_class_switching

Description: Checks if the network has class switching

Syntax:

sn_has_class_switching(...)

sn_has_closed_classes

Description: Checks if the network contains closed classes

Syntax:

sn_has_closed_classes(...)

sn_has_dps

Description: Checks if the network uses Discriminatory Processor Sharing

Syntax:

sn_has_dps(...)

sn_has_dps_prio

Description: Checks if the network uses DPS with priorities

Syntax:

sn_has_dps_prio(...)

sn_has_fcfs

Description: Checks if the network has FCFS scheduling

Syntax:

sn_has_fcfs(...)

sn_has_fork_join

Description: Checks if the network contains fork-join nodes

Syntax:

sn_has_fork_join(...)

sn_has_fractional_populations

Description: Checks if the network has fractional population values

Syntax:

sn_has_fractional_populations(...)

sn_has_gps

Description: Checks if the network uses GPS scheduling

Syntax:

sn_has_gps(...)

sn_has_gps_prio

Description: Checks if the network uses GPS with priorities

Syntax:

sn_has_gps_prio(...)

sn_has_hol

Description: Checks if the network uses HOL scheduling

Syntax:

sn_has_hol(...)

sn_has_homogeneous_scheduling

Description: Checks if all stations use the same scheduling policy

Syntax:

sn_has_homogeneous_scheduling(...)

sn_has_inf

Description: Checks if the network has infinite server stations

Syntax:

sn_has_inf(...)

sn_has_lcfs

Description: Checks if the network uses LCFS scheduling

Syntax:

sn_has_lcfs(...)

sn_has_lcfs_pi

Description: Checks if the network uses LCFS with preemptive-identical scheduling

Syntax:

sn_has_lcfs_pi(...)

sn_has_lcfs_pr

Description: Checks if the network uses LCFS with preemptive-resume scheduling

Syntax:

sn_has_lcfs_pr(...)

sn_has_lept

Description: Checks if the network uses LEPT scheduling

Syntax:

sn_has_lept(...)

sn_has_ljf

Description: Checks if the network uses LJF scheduling

Syntax:

sn_has_ljf(...)

sn_has_load_dependence

Description: Checks if the network has load-dependent service rates

Syntax:

sn_has_load_dependence(...)

sn_has_mixed_classes

Description: Checks if the network has both open and closed classes

Syntax:

sn_has_mixed_classes(...)

sn_has_multi_chain

Description: Checks if the network has multiple chains

Syntax:

sn_has_multi_chain(...)

sn_has_multi_class_fcfs

Description: Checks if the network has multi-class FCFS stations

Syntax:

sn_has_multi_class_fcfs(...)

sn_has_multi_class_heter_exp_fcfs

Description: Checks for multi-class FCFS with heterogeneous exponential service

Syntax:

sn_has_multi_class_heter_exp_fcfs(...)

sn_has_multi_class_heter_fcfs

Description: Checks for multi-class FCFS with heterogeneous service

Syntax:

sn_has_multi_class_heter_fcfs(...)

sn_has_multi_class

Description: Checks if the network has multiple classes

Syntax:

sn_has_multi_class(...)

sn_has_multiple_closed_classes

Description: Checks if the network has multiple closed classes

Syntax:

sn_has_multiple_closed_classes(...)

sn_has_multi_server

Description: Checks if the network has multi-server stations

Syntax:

sn_has_multi_server(...)

sn_has_open_classes

Description: Checks if the network contains open classes

Syntax:

sn_has_open_classes(...)

sn_has_priorities

Description: Checks if the network uses priority scheduling

Syntax:

sn_has_priorities(...)

sn_has_product_form

Description: Checks if the network has product-form solution

Syntax:

sn_has_product_form(...)

sn_has_product_form_not_het_fcfs

Description: Checks for product-form excluding heterogeneous FCFS

Syntax:

sn_has_product_form_not_het_fcfs(...)

sn_has_ps

Description: Checks if the network uses PS scheduling

Syntax:

sn_has_ps(...)

sn_has_ps_prio

Description: Checks if the network uses PS with priorities

Syntax:

sn_has_ps_prio(...)

sn_has_sept

Description: Checks if the network uses SEPT scheduling

Syntax:

sn_has_sept(...)

sn_has_single_chain

Description: Checks if the network has a single chain

Syntax:

sn_has_single_chain(...)

sn_has_single_class

Description: Checks if the network has a single class

Syntax:

sn_has_single_class(...)

sn_has_siro

Description: Checks if the network uses SIRO scheduling

Syntax:

sn_has_siro(...)

sn_has_sjf

Description: Checks if the network uses SJF scheduling

Syntax:

sn_has_sjf(...)

sn_is_closed_model

Description: Checks if the network is a closed model

Syntax:

sn_is_closed_model(...)

sn_is_mixed_model

Description: Checks if the network is a mixed model

Syntax:

sn_is_mixed_model(...)

sn_is_open_model

Description: Checks if the network is an open model

Syntax:

sn_is_open_model(...)

sn_is_population_model

Description: Checks if the network is defined by populations

Syntax:

sn_is_population_model(...)

sn_is_state_valid

Description: Validates a network state

Syntax:

isvalid = sn_is_state_valid(sn)

Parameters:

Name	Description
sn	Stochastic network structure

Returns:

Name	Description
isvalid	Validation flag (boolean)

sn_print

Description: Prints comprehensive information about a NetworkStruct object

Syntax:

function sn_print(sn)

Parameters:

Name	Description
sn	Stochastic network structure

sn_print_routing_matrix

Description: Prints the routing matrix of the network

Syntax:

function sn_print_routing_matrix(sn, onlyclass)

Parameters:

Name	Description
sn	Stochastic network structure
onlyclass	Restrict computation to specific class

sn_refresh_visits

Description: Solves traffic equations to compute visit ratios

Syntax:

[visits, nodevisits, sn] = sn_refresh_visits(sn, chains, rt, rtnodes)

Parameters:

Name	Description
sn	Stochastic network structure
chains	Chain indices or chain structure
rt	Response time values
rtnodes	Routing nodes

Returns:

Name	Description
visits	Visit counts or ratios
nodevisits	Visit counts per node
sn	Stochastic network structure

sn_rtnodes_to_rtorig

Description: Converts node routing matrix to the original routing matrix format

Syntax:

[rtorigcell, rtorig] = sn_rtnodes_to_rtorig(sn)

Parameters:

Name	Description
sn	Stochastic network structure

Returns:

Name	Description
rtorigcell	Original routing as cell array
rtorig	Original routing matrix