teletraffic 1.0.0

Main teletraffic functions

teletraffic

Python library for calculating performance measures of queueing systems using analytical formulas and simulation methods.

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Installation

pip install teletraffic

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Supported models and functions

E — Erlang B formula

Description: Erlang B loss probability formula.

Arguments:

• z — offered traffic from a group of users, [Erl]
• v — number of servers

Result:

• p — call loss probability

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Hi — Palm–Jacobaeus formula

Arguments:

• z — offered traffic from a group of users, [Erl]
• v — number of servers
• d — number of busy servers

Result:

• p — call loss probability

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PalmTable — Palm loss table

Arguments:

• z — offered traffic from a group of users, [Erl]
• v — number of servers

Result:

• p — call loss probability

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M_M_V_L_an — Analytical M/M/V/L model (Kendall–Basharin notation)

Arguments:

• z — offered traffic from a group of users, [Erl]
• v — number of servers

Properties:

• loss — call loss probability
• serv — carried traffic, [Erl]

Methods:

• show() — display QoS characteristics of the analytical M/M/V/L model

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M_M_V_L_im — Simulation M/M/V/L model (Kendall–Basharin notation)

Arguments:

• z — offered traffic from a group of users, [Erl]
• v — number of servers
• nz — number of simulated calls
• seed — random seed (default: 0)

Properties:

• loss — call loss probability
• serv — carried traffic, [Erl]

Methods:

• show() — display QoS characteristics of the simulation M/M/V/L model

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EngsetTable — Engset loss table

Arguments:

• z — offered traffic per user, [Erl]
• n — number of users
• v — number of servers

Result:

• p — call loss probability

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Mi_M_V_L_an — Analytical Mi/M/V/L model

Arguments:

• z — offered traffic per user, [Erl]
• n — number of users
• v — number of servers

Properties:

• loss — call loss probability
• serv — carried traffic, [Erl]

Methods:

• show() — display QoS characteristics of the analytical Mi/M/V/L model

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VM_M_V_L_PRA_an — Analytical VM/M/V/L/PRA model

Arguments:

• vz — vector of offered traffic intensities by service class, [Erl]
• v — number of servers

Properties:

• vloss — vector of call loss probabilities by service class
• serv — carried traffic, [Erl]

Methods:

• show() — display QoS characteristics of the analytical VM/M/V/L/PRA model

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M_G_V_L_an — Analytical M/G/V/L model

Arguments:

• ts — mean service time
• tbr — mean time to failure of a server
• trec — mean recovery time of a server
• lmb — arrival rate
• v — number of servers

Properties:

• loss — call loss probability
• serv — carried traffic, [Erl]

Methods:

• show() — display QoS characteristics of the analytical M/G/V/L model

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ErlangFormula2 — Erlang second formula

Arguments:

• z — offered traffic from a group of users, [Erl]
• v — number of servers

Result:

• p — call loss probability

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M_M_V_W_FF_R_an — Analytical M/M/V/W/FF/R model

Arguments:

• z — offered traffic from a group of users, [Erl]
• v — number of servers
• ta — admissible waiting time
• ts — mean service time

Properties:

• wait — waiting probability
• over_wait — probability of waiting longer than admissible time
• avr_time — average waiting time
• avr_time_wait — average waiting time for waiting calls
• queue — probability of a non-empty queue

Methods:

• show() — display QoS characteristics of the analytical M/M/V/W/FF/R model

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M_M_V_W_FF_R_im — Simulation M/M/V/W/FF/R model

Arguments:

• z — offered traffic from a group of users, [Erl]
• v — number of servers
• nz — number of simulated calls
• ta — admissible waiting time (default: 0)
• seed — random seed (default: 0)

Properties:

• wait — waiting probability
• over_wait — probability of waiting longer than admissible time
• avr_time — average waiting time
• avr_time_wait — average waiting time for waiting calls
• queue — probability of a non-empty queue

Methods:

• show() — display QoS characteristics of the simulation M/M/V/W/FF/R model

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VM_VMl_V_L_an — Analytical multiservice VM/VMl/V/L model (full accessibility)

Arguments:

• vz — vector of offered traffic intensities, [Erl]
• vb — vector of bandwidth requirements per service class, [CRU]
• kc — number of traffic groups
• f — capacity of a traffic group, [CRU]

Properties:

• vloss — vector of call loss probabilities by service class
• serv — carried traffic, [Erl]

Methods:

• show() — display QoS characteristics of the analytical VM/VMl/V/L model

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VM_VMl_VDg_L_an — Analytical multiservice VM/VMl/VDg/L model (limited accessibility)

Arguments:

• vz — vector of offered traffic intensities, [Erl]
• vb — vector of bandwidth requirements per service class, [CRU]
• kc — number of traffic groups
• f — capacity of a traffic group, [CRU]
• kd — number of traffic groups accessible to each service class

Properties:

• vloss — vector of call loss probabilities by service class
• serv — carried traffic, [Erl]

Methods:

• show() — display QoS characteristics of the analytical VM/VMl/VDg/L model

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VM_VMl_VDg_L_im — Simulation multiservice VM/VMl/VDg/L model (limited accessibility)

Arguments:

• vz — vector of offered traffic intensities, [Erl]
• vb — vector of bandwidth requirements per service class, [CRU]
• kc — number of traffic groups
• f — capacity of a traffic group, [CRU]
• kd — number of traffic groups accessible to each service class
• nz — number of simulated calls
• strategy — channel allocation strategy ("МаксСвоб", "МинСвоб", "ПервСвоб")

Properties:

• vloss — vector of call loss probabilities by service class
• serv — carried traffic, [Erl]

Methods:

• show() — display QoS characteristics of the simulation VM/VMl/VDg/L model

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Quick start

import teletraffic as ttt

print(ttt.E(9, 5))
print(ttt.Hi(9, 5, 3))
print(ttt.PalmTable(9, 5))

A = ttt.M_M_V_L_an(9, 5)
B = ttt.M_M_V_L_im(9, 5, 1_000_000)
B = ttt.M_M_V_L_im(9, 5, 1_000_000, 0)

print(ttt.EngsetTable(0.4, 10, 5))

C = ttt.Mi_M_V_L_an(0.4, 10, 5)
D = ttt.VM_M_V_L_PRA_an([2, 0.4], 3)
E = ttt.M_G_V_L_an(0.2, 34, 2, 44, 10)

print(ttt.ErlangFormula2(1, 3))

F = ttt.M_M_V_W_FF_R_an(1, 2, 0.05, 0.2)
J = ttt.M_M_V_W_FF_R_im(0.7, 2, 1_000_000)
H = ttt.M_M_V_W_FF_R_im(0.7, 2, 1_000_000, 0)
K = ttt.M_M_V_W_FF_R_im(0.7, 2, 1_000_000, 0, 0)

L = ttt.VM_VMl_V_L_an([10, 12], [1, 5], 3, 20)
M = ttt.VM_VMl_VDg_L_an([10, 12], [1, 5], 3, 20, 2)
N = ttt.VM_VMl_VDg_L_im([10, 12], [1, 5], 3, 20, 2, 100_000, "ПервСвоб")

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Analytical vs simulation methods

Functions ending with _an use analytical formulas. Functions ending with _im use simulation methods.