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Erlang C / B Functions in Python

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Erlang C for Python

This Erlang Python Library was created to enable Erlang based contact center forecasting using Python.

Table of Contents

  1. Erlang C Definition
  2. Library Overview
  3. Classes
  4. Erlang Base Class
  5. MinMax Method
  6. Erlang Main Class
  7. Introduction
  8. ErlangB - calculate probability of call being blocked
  9. ErlangBExt - calculate probability of call being blocked
  10. EngsetB - calculate probability of call being blocked
  11. ErlangC - calculate probability of transaction being queued
  12. NBTrunks - Calculate number of trunks - use for high volume
  13. NumberTrunks - Calculate number of trunks - use for normal volume
  14. NumberAgents - Calculate the number of agents
  15. LoopingTraffic
  16. Abandon
  17. Agents
  18. AgentASA
  19. ASA
  20. CallCapacity
  21. FractionalAgents
  22. FractionalCallCapacity
  23. Queued
  24. QueueSize
  25. QueueTime
  26. ServiceTime
  27. SLA
  28. Trunks
  29. Utilisation

Definition of Erlang C

Erlang C is a telephony traffic concept that can be used in call center management. It is based on the concept of an Erlang, a virtual unit of telephony that represents a certain workload on a system. In many uses, “Erlang” refers to a metric involving call minutes.

Erlang C is a proven method or formula to successfully predict call center load and can be used in call center management. The Erlang C formula calculates based on basic information (like the expected number of incidents) how many service representatives (or agents) are needed to meet your desired service level. It is based on the concept of an Erlang, a virtual unit of telephony that represents a certain workload on a system. In many uses, “Erlang” refers to a metric involving call minutes. Erlang C is the standard in the contact center industry.

In Erlang C, planners calculate three factors. One is the number of lines available to intake calls, which are staffed by call-center operators. Another is the number of callers waiting for service. The third piece of the equation is the average time to serve every caller.

Erlang C can be instructive in large-scale call centers and in other virtual telephony environments. Different types of call handling software can deal with delays such as busy signals and dropped calls. Using metrics like Erlang C, call center managers can make these operations as efficient as possible, which can be a big and important part of serving inbound callers in industries such as telecommunications, retail, government services or any place where service takes place by phone.

Library Overview

With this Python Class, one can calculate a variety of parameters affecting contact center operations and customer experience. As a general note, Erlang was developed mainly with phone conversations in mind, but to a wide extend can also be used for the same kind of calculations for contact centers that are not phone based, but have channels such as chat, email, social media and messengers. I use transactions where a customer might use any channel, and calls where a customer uses phone. Some of the calculations are only relevant for voice contact centers, such as the number of Trunk lines (I will call those out that are only relevant for phone).

Here is a list contact center variables that can be calculated using this Erlang Class:

  • Number of Agents required to handle a given number of transactions in a given interval;
  • Service Level that will be achieved with a number of agents and a given transaction volume;
  • Queue times - how long will a customer typically have to wait to get through to an agent;
  • Queue size - how many customers will on average be put in a queue given number of agents, SLA, AHT and other parameters;
  • How many interactions will be queued on average given the number of agents, SLA, AHT and other parameters;
  • Average Speed to Answer;
  • Abandonment Rate;
  • Given a call volume, how many Trunk lines are required to achieve SLA, ASA, Abandon and other parameters;
  • and more...

Classes

The Library contains two main classes:

  • Erlang-Base class contains base modules required by both, Erlang-B and Erlang-C classes;
  • Erlang class contains all modules required to conduct Erlang-B/-C calculations;

The code was developed on a Mac using OneDrive as the repository. For all includes to work accordingly, the following directory structure would have to be recreated:

⋅⋅⋅/Users/(username)/OneDrive/Development/Python/Erlang

Erlang Base Class

MinMax

MinMax(Eval, Min, Max) - Method evaluates Eval against Min and Max.

Returns (float)

  • Min if Eval is less than Min
  • Max if Eval is larger than Max
  • Otherwise Eval

Erlang Main Class

Introduction

The Erlang Class regards the fact that when using chat or email or other non-voice media an agent can handle more than one transaction at any given time. This fact is controlled by the parameters given to the __init__(..., nv, ccc,...) method of the Erlang Class. The parameter nv, if it is set to true, indicates that the object created from this Class is a non-voice calculation. The ccc parameter defines the amount of concurrent transactions agents on average can handle.

IMPORTANT

The implication of this is that the class cannot be reused for different media types. If, for example one would have to calculate the numbers for a call center, then one would create an object with parameters nv = false and ccc = 1 - meaning voice and concurrent calls = 1. If then one would have to calculate the parameters for a chat support group, the previous object of Class Erlang would have to be destroyed and a new object with parameters nv = true and ccc = 3 - meaning non-voice and concurrent transactions = 3. Internally, the provided methods will check for these 2 parameters and change calculation methods accordingly. The approach taken here is that the given AIT (Average Interaction Time aka ATT - Average Talk Time) is divided by the number of concurrent actions an agent can handle. This effectively is the same result as if the number of agents would be increased to 3 (in this >example); however, the benefit of changing the AIT is that each agent will still have the same after transaction wrap time, so the the result is more precise.

NOTE

Throughout this document the following terms have the meaning as defined below:

  • Arrival Rate is the number of Transactions arriving per interval.
  • Completion Rate is the number of Transactions completed per interval.
  • Transactions any transaction that has been initiated by customers. This may be a phone call, an email, a chat session, or social media session, depending on the channels supported by the contact center.
  • Death Rate has the same meaning as Completion Rate.
  • Server or Servers is defined as a single entity or multiple entities which can service transactions, typically an agent.
  • SLA is the Service Level that the contact center tries to achieve. SLA would be contractually fixed and is measured in percentage of offered transactions answered in a defined period. For example 80/20 means 80% of transactions need to be answered in 20 seconds.
  • Utilisation is the level of time a server or agent is actually delivering work compared to the interval the agent is available. E.g. a 50% utilisation would mean that an agent how is working for 1 hour is only delivering actual work for 30 minutes.
  • Abandon defines that a customer contacting the contact center interrupts or abandons the transaction before a server or agent can attend to them. This is typically the case if wait times in a queue are too long.

The methods of the classes are described below. If you want to learn how to use the Erlang library in your Python code please refer to the How to guide

ErlangB

ErlangB (servers, intensity) - The Erlang B formula calculates the percentage likelihood of the call being blocked, that is that all the trunks are in use and the caller will receive a busy signal.

Parameters

  • servers = Number of telephone lines
  • intensity = Arrival rate of calls / Completion rate of calls

Returns (float) - the percentage likelihood of a call being blocked

ErlangBExt

ErlangBExt (servers, intensity, retry) - the Extended Erlang B formula calculates the percentage likelihood of the call being blocked, that is all the trunks are in use and the caller will receive a busy signal. The Extended version allows input of a percentage figure for those blocked callers who will immediately retry.

Parameters

  • servers = Number of telephone lines
  • intensity = Arrival rate of calls / Completion rate of calls
  • retry = Number of blocked callers who will retry immediately (0.1 = 10%)

Returns (float) - The probability in % of a call being blocked.

EngsetB

EngsetB (servers, intensity) - the Engset B formula calculates the percentage i of the call being blocked, that is that all the trunks are in use and the caller will receive a busy signal. This uses the Engset model, based on the hindrance formula.

Parameters

  • servers = Number of telephone lines
  • events = Number of calls or transactions
  • intensity = Arrival rate of calls / Completion rate of calls

Returns (float) - the probability in % of a call being blocked.

ErlangC

ErlangC (agents, intensity) - this formula gives the percentage likelihood of the transaction (call, chat, social media tx) being placed in a queue.

Parameters<

  • agents = Number of agents
  • intensity = Arrival rate of transactions / Completion rate of calls

Returns (float) - the probability in % of a transaction being placed in a queue.

NBTrunks

NBTrunks (intensity, blocking) - this function has been supplied by Edwin Barendse. This formula gives the number of telephone lines required to handle the high volume traffic in Erlang against a required blocking factor.

Parameters

  • blocking = blocking factor percentage e.g. 0.10 (10% of calls may receive busy tone)
  • intensity = Arrival rate of transactions / Completion rate of calls

Returns (float) - the number of telephone lines required.

NumberTrunks

NumberTrunks (intensity, blocking) - this formula gives the maximum number of telephone trunks required to handle the answered and queuing calls (up to a maximum of 255).

Parameters

  • agents = Number of Agents
  • intensity = Busy hour traffic - Arrival rate of transactions / Completion rate of calls

Returns (int) - the max number of telephone lines required.

NumberAgents

NumberAgents (intensity, blocking) - the formula calculates the number of servers required to service the given traffic intensity with the given blocking factor.

Parameters

  • agents = Number of Agents
  • blocking = blocking factor percentage e.g. 0.10 (10% of calls may receive busy tone)

Returns (int) - the number of agents required.

LoopingTraffic

LoopingTraffic (trunks, blocking, increment, min_int) - this function tries values from min_int to max_int, increasing the traffic by increment until the approximate blocking is found, processing then loops with stepping of increment/10 (e.g. 10, 1, 0.1, 0.01, 0.001) until the value is found to the precision required (defined by constant MaxAccuracy).

Parameters

  • trunks = number of Trunk lines
  • blocking = blocking factor percentage e.g. 0.10 (10% of calls may receive busy tone)
  • increment = traffic increase increment
  • min_int = Minimum traffic intensity

Returns (float) - the appropriate blocking value.

Adandon

Adandon (agents, transactions) - this method calculates the percentage of transactions which will be abandoned after the time given. It regards the fact that when using chat or email or other non-voice media an agent can handle more than one transaction at any given time. This fact is controlled by the parameters given to the __init__(...) method of the Erlang Class, refer here for more details.

Parameters

  • agents = number of agents available
  • transactions = number of calls received in the interval period

    Parameters provided in constructor

    • ABANDON TIME the time in seconds before the caller will abandon and is given when creating an object from this Class.
    • AHT is the call duration including after call work in seconds e.g 180 and is given when creating an object from this Class.
    • INTERVAL is the forecasting interval 15, 30, 45, 60 minutes and is given when creating an object from this Class.

Returns (float) - Percentage of calls abandoned within interval.

Agents

Agents (service_time, transactions) - calculates the number of agents required to service a given number of transactions to meet a given service level. It regards the fact that when using chat or email or other non-voice media an agent can handle more than one transaction at any given time. This fact is controlled by the parameters given to the __init__(...) method of the Erlang Class, refer here for more details.

Parameters

  • service_time = target answer time in seconds e.g. 15
  • transactions = the number of transactions received in the given interval period

    Parameters provided in constructor

    • SLA is the % of calls to be answered within the ServiceTime period e.g. 0.95 (95%) and is given when creating an object from this Class.
    • AHT is the call duration including after call work in seconds e.g 180 and is given when creating an object from this Class.

Returns (int) - number of agents required

AgentASA

AgentASA (asa, transactions) - calculate the number of agents required to service a given number of calls to meet the average speed of answer. It regards the fact that when using chat or email or other non-voice media an agent can handle more than one transaction at any given time. This fact is controlled by the parameters given to the __init__(...) method of the Erlang Class, refer here for more details.

Parameters

  • asa = the Average Speed of Answer in seconds.
  • transactions = the number of transactions received in the given interval period.

    Parameters provided in constructor

    • SLA is the % of calls to be answered within the ServiceTime period e.g. 0.95 (95%).
    • AHT is the call duration including after call work in seconds e.g 180.

Returns (int) - Number of agents required per interval to meet ASA

ASA

ASA (agents, transactions) - function calculates the Average Speed to Answer (ASA) for the given number of agents.

Parameters

  • agents = number of agents available
  • transactions = the number of transactions received in the given interval period.

    Parameters provided in constructor

    • AHT is the call duration including after call work in seconds e.g 180 and is given when creating an object from this Class.
    • INTERVAL is the forecasting interval 15, 30, 45, 60 minutes and is given when creating an object from this Class.

Returns (int) - the average speed to answer in seconds.

CallCapacity

CallCapacity (agents, service_time) - function calculates the number of calls which can be handled by the given number of agents whilst still achieving the grade of service.

Parameters

  • agents = number of agents available
  • service_time = target answer time in seconds e.g. 15

    Parameters provided in constructor

    • AHT is the call duration including after call work in seconds e.g 180 and is given when creating an object from this Class.
    • SLA is the % of calls to be answered within the ServiceTime period e.g. 0.95 (95%).
    • INTERVAL is the forecasting interval 15, 30, 45, 60 minutes and is given when creating an object from this Class.

Returns (int) - the average speed to answer in seconds.

FractionalAgents

FractionalAgents (service_time, transactions) - function calculates the number of calls which can be handled by the given number of agents whilst still achieving the grade of service.

Parameters

  • service_time = target answer time in seconds e.g. 15
  • transactions = the number of transactions received in the given interval period

    Parameters provided in constructor

    • AHT is the call duration including after call work in seconds e.g 180 and is given when creating an object from this Class.
    • SLA is the % of calls to be answered within the ServiceTime period e.g. 0.95 (95%).
    • INTERVAL is the forecasting interval 15, 30, 45, 60 minutes and is given when creating an object from this Class.

Returns (int) - the average speed to answer in seconds.

FractionalCallCapacity

FractionalCallCapacity (service_time, agents) - function calculates the number of calls which can be handled by the given number of agents whilst still achieving the grade of service.

Parameters

  • service_time = target answer time in seconds e.g. 15
  • agents = number of agents available

    Parameters provided in constructor

    • AHT is the call duration including after call work in seconds e.g 180 and is given when creating an object from this Class.
    • SLA is the % of calls to be answered within the ServiceTime period e.g. 0.95 (95%).
    • INTERVAL is the forecasting interval 15, 30, 45, 60 minutes and is given when creating an object from this Class.

Returns (int) - the average speed to answer in seconds.

Queued

Queued (agents, transactions) - function calculates the percentage of calls which will queue for the given number of agents.

Parameters

  • agents = number of agents available
  • transactions = the number of transactions received in the given interval period

    Parameters provided in constructor

    • AHT is the call duration including after call work in seconds e.g 180 and is given when creating an object from this Class.
    • INTERVAL is the forecasting interval 15, 30, 45, 60 minutes and is given when creating an object from this Class.

Returns (float) - the percentage of calls which will queue for the given number of agents.

QueueSize

QueueSize (agents, transactions) - function calculates the average queue size for a given number of agents.

Parameters

  • agents = number of agents available
  • transactions = the number of transactions received in the given interval period

    Parameters provided in constructor

    • AHT is the call duration including after call work in seconds e.g 180 and is given when creating an object from this Class.
    • INTERVAL is the forecasting interval 15, 30, 45, 60 minutes and is given when creating an object from this Class.

Returns (int) - the average queue size for a given number of agents.

QueueTime

QueueTime (agents, transactions) - function calculates the average queue time for those calls which will queue.

Parameters

  • agents = number of agents available
  • transactions = the number of transactions received in the given interval period

    Parameters provided in constructor

    • AHT is the call duration including after call work in seconds e.g 180 and is given when creating an object from this Class.
    • INTERVAL is the forecasting interval 15, 30, 45, 60 minutes and is given when creating an object from this Class.

Returns (int) - the average queue time for those calls which will queue.

ServiceTime

ServiceTime (agents, transactions) - function calculates the average waiting time in which a given percentage of the calls will be answered.

Parameters

  • agents = number of agents available
  • transactions = the number of transactions received in the given interval period

    Parameters provided in constructor

    • AHT is the call duration including after call work in seconds e.g 180 and is given when creating an object from this Class.
    • INTERVAL is the forecasting interval 15, 30, 45, 60 minutes and is given when creating an object from this Class.
    • SLA is the % of calls to be answered within the ServiceTime period e.g. 0.95 (95%).

Returns (int) - the average waiting time in which a given percentage of the calls will be answered.

SLA

SLA (agents, transactions) - function calculates the service level achieved for the given number of agents.

Parameters

  • agents = number of agents available
  • transactions = the number of transactions received in the given interval period

    Parameters provided in constructor

    • AHT is the call duration including after call work in seconds e.g 180 and is given when creating an object from this Class.
    • INTERVAL is the forecasting interval 15, 30, 45, 60 minutes and is given when creating an object from this Class.

Returns (float) - the service level achieved for the given number of agents.

Trunks

Trunks (agents, transactions) - function calculates the number of telephone lines required to service a given number of calls and agents.

  • Parameters
  • agents = number of agents available
  • transactions = the number of transactions received in the given interval period
    • Parameters provided in constructor
    • AHT is the call duration including after call work in seconds e.g 180 and is given when creating an object from this Class.
    • INTERVAL is the forecasting interval 15, 30, 45, 60 minutes and is given when creating an object from this Class.

Returns (int) - the number of telephone lines required to service a given number of calls and agents.

Utilisation

Utilisation (agents, transactions) - function calculates the utilisation percentage for the given number of agents.

  • Parameters
  • agents = number of agents available
  • transactions = the number of transactions received in the given interval period
    • Parameters provided in constructor
    • AHT is the call duration including after call work in seconds e.g 180 and is given when creating an object from this Class.
    • INTERVAL is the forecasting interval 15, 30, 45, 60 minutes and is given when creating an object from this Class.

Returns (float) - the utilisation percentage for the given number of agents.

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Erlang C / B Functions in Python

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