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Queuing Theory

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1. What is Queuing Theory?

It’s a way of determining how to better handle situations where clients are waiting to be served. Queuing models are used to determine the average wait time and the average queue length. These measures are used to assess customer satisfaction and how well resources are utilised. Queuing theory is based on three things,

  1. A queuing model that mathematically represents queue characteristics and variables, i.e. wait time, number of available resources & probability of events.
  2. A real-world system such as a telephone network, bank or call centre.
  3. A mapping between the two.

2. Queuing Notation

Queuing models are represented using Kendall’s A/B/C notation

  • A. The arrival time distribution.
  • B. The service time distribution.
  • C. The number of servers i.e. .number of resources providing a service.

K, N and D were later added to the model to make it A/B/C/K/N/D

  • K. The number of customers in the system at any given point of time.
  • N. The population of people who could be requesting service.
  • D. The order in which customers are served e.g. FIFO.

In most models, K, N and D are assumed to be,

  • K. Infinite.
  • N. Infinite. 
  • D. FIFO (First In, First Out).

3. Common Notations

There are three common notations that are plugged into the A and B variables,

  1. Deterministic, inter-arrival time and service-times are a Constant.
  2. Markovian, inter-arrival time and service-times are Exponential .
  3. General, inter-arrival and service-times are any distribution.

4. Different Queuing Types

There are four different queuing model types,

  1. Single-Channel, Single-Phase used for resource skills that are simple.
  2. Single-Channel, Multiple-Phase used for resource skills that are complex.
  3. Multiple-Channel, Single-Phase used for simple team resource skills.
  4. Multiple-Channel, Multiple-Phase used for complex team resource skills.

5. Queuing Model

The project arrival and project delivery rates are modelled. Also, the number and type of project resources available and the design of project services offered needs to be modelled. Marketing and psychological data needs either be estimated else gathered to ensure the abstract model reflects reality as closely as possible. Having developed a model, it can then be experimented with to determine how changing different factors affects client outcomes, which then leads to an optimised model.

6. Queuing Performance

Project organisations constantly struggle between quality of service provided versus the efficiency of operations. Considerations of resource supply versus project demand is a dynamic activity reflecting uncertainty in project arrivals and how projects perform. Further complications involve resource capacity versus capability which is dependent on the nature and types of projects in the portfolio. Queuing models help balance these considerations by incorporating the economic impact of adding more staff versus what the market is will to pay.

7. Staffing Levels

Queuing theory helps project organisations hire new resources and schedule projects. During any given project, a certain skill may be in demand and for proper staffing you need skill sets to overlap so all client needs can be met at any given time. When modelling organisation capacity it is tempting to assume a best-case scenario however our experience indicates it is better to set the floor for minimum capacity and then anything chargeable and billable over and beyond this is a bonus. A further tip is to account for public holidays, annual leave, training and sick leave.

8. Queuing Challenges

It is not possible to rely solely on queuing theory for optimal solutions for planning project services. The old adage, “all models are wrong, but some are useful” springs to mind. Models are an abstraction of reality and hence do not perfectly model all real-life scenarios. Consequently, while underlying patterns of project service can be modelled, not all real-life scenarios follow an exact pattern, which can result in unpredictable behaviour and results.

9. Queuing Psychology

Research shows that how people “feel” while waiting in a queue matters more than the length of the wait. In other words, the “experience” of waiting is more important than the actual “time” spent waiting. By leveraging knowledge on the psychology on queuing, you can ensure customer user experiences are always positive.

10. Queuing Readiness Signs

Five signs your organisation is not only ready but in need of a queuing model,

  1. Your customers are not being served quick enough.
  2. Your project services loads are out of balance.
  3. You are unable to predict queue bottlenecks.
  4. Your customers complain about your queue.
  5. Your managers are uninformed.

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