Queueing Models

Introduction

Erlang-C is the best-known queueing model for call-centres and other real-life queueing situations. There are a number of other models available in PhoneCalc related programs, dealing with different queueing situations.

Basic Queued Calls (Erlang-C)

Basic Lost Calls (Erlang-B)

Basic Call Retry (Erlang-B Extended)

Abandoned Calls (Mitan-C)

Limited Queue Size

Overflow on Timeout

Advanced Call Retry.

Erlang-C (Basic Queued Calls)

Erlang-C is the formula conventionally used in call-centres to work out how many agents are needed to achieve the target service level. Arriving calls are answered immediately if an agent is available, otherwise the calls join the queue. Calls are answered first-come first-served. Callers never abandon or get removed from the system except by being answered by an agent. There is no limit Erlang-C doesn't work if the call load exceeds the capacity of the agents. There is no "safety-valve" of any kind to deal with overload situations.

An important limitation of Erlang-C is that it can tell you nothing about abandoned calls. It is extremely misleading to believe that Erlang-C can tell you anything at all about abandon rates. Erlang-C is widely used because it is quite easy to program and provides a rough guide to the number of agents needed, but Erlang-C is an unnecessary over-simplification, and for general call-centre use Mitan-C is better.

Erlang-B ( Basic Lost Calls )

With the Basic Lost Calls model, calls are not allowed to queue if there is no agent available when the call arrives. Calls arriving when all the agents are busy are "lost", which means they get a busy tone. Lost calls are not re-tried.

The Basic Lost Calls model can be used for calculating the number of phone lines needed. For this application an "agent" is really a phone line. You could use a maximum loss rate of 1%, and this would give you some idea of how many phone l

Erlang-B Extended (Basic Retry)

The Basic Retry model is a way of taking into account callers attempting a call again when they get a busy tone. A call attempt is said to be "blocked" if there is no agent avaiable when the call arrives. The caller may then decide to retry

The Basic Retry model will still tend to under-estimate the loss or abandon rate, beacuse it does not take into account the fact that another call attempt is often made within a few seconds of a failed call attempt. This means in practice t

Limited Queue Size

With the limited queue size model, the number of calls waiting is restricted to a specified maximum size. In general, this improves the service level for those calls that are allowed to enter the queue, at the expense of a small proportion

Limited Waiting Time

With the limited waiting time model, the length of time that a call may wait is limited to a specified maximum size. In general, this improves the service level for most calls, at the expense of a small proportion of calls that are disconne

Mitan-C (Abandoned Calls)

The Abandoned Calls (Mitan-C) model is a "super" version of Erlang-C. Mitan-C takes account of the tolerance, or impatience, of callers. The interaction between service-level and abandon rate is complex and subtle, and cannot be accounted f

Advanced Retry/

The Advanced Retry model deals with the situation in which calls are not queued, and receive busy tone if all the agents are busy. This model takes account of both the proportion of failed calls that retry, and the average time between retr

Note
The Advanced Retry model requires extensive calculations. For this reason, the number of agents is currently limited to 1000. Users who need to use this model with more than 1000 agents should contact Mitan Ltd.