Project Services Queuing Model

Ideally project arrival & delivery times would be certain. In reality, both are uncertain resulting in long queues & wait times that frustrate clients.

Project Services Queuing Model

Queues only form because not enough resources are available when a project is needed.

Project Services Queuing Model

To better understand how congestion builds in a project services organisation four scenarios will be explored,

  • Scenario #1: Certain project arrival and certain project delivery times.
  • Scenario #2: Certain project arrival and uncertain project delivery times.
  • Scenario #3: Uncertain project arrival and certain project delivery times.
  • Scenario #4: Uncertain project arrival and uncertain project delivery times.

For this model, it’s assumed a project services organisation receives 40 project requests a week and that a single person can deliver 50 projects per week i.e. on average, this person will be 80% utilised. Importantly, this organisation does not prioritise projects and instead adopts a first-come-first-served policy. Finally, to keep the model simple, it is assumed clients neither baulk nor renege once they join the queuing system.

Certain project arrival rates and certain delivery times are modelled using a Constant distribution, while uncertain project arrival rates are modelled using a Poisson distribution and uncertain project delivery times are modelled using an exponential distribution.

Project Services Queuing Simulation

The following is a simulation showing how queues form in a 40-hour period for each of the scenarios.

Project Services Queuing Results

All project service queuing systems are non-terminating meaning they don’t have a natural or obvious end time, i.e. the queue does not clear. The following are the results of an extended simulation that allowed the model to reach steady-state by clearing the results of the warm-up period.

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  • Scenario #1: Queues never form as one project arrives another leaves the system, meaning projects are only in the system for 0.8 hours.
  • Scenario #2: Queues form because of uncertain delivery times and while the average results are probably tolerable the maximum results, especially for wait times is likely to be a concern.
  • Scenario #3: Queues form because of uncertain arrival times with all performance indicators being worse than scenario #2 except for the maximum wait times. While project organisations can take steps to minimise uncertainty in their project deliveries, it is much harder to manage client project arrival demand.
  • Scenario #4: Queues form because of uncertainty in both arrival and delivery times. These simulation results very closely align with those mathematically calculated and show the potential client frustration that will inevitably result from long queues and long wait times. While not modelled here, it is unlikely that clients in this scenario will remain in the system and will almost certainly renege once they get fed up with waiting too long for their project to be delivered.

Project Services Queuing Summary

While the generalisations for this simplified model are intuitive, actual results are likely to be alarming. This is because the project resource is not maxed out and instead is only 80% utilised, i.e. project demand does not exceed resource capacity, nonetheless queues form with very long wait times when there is uncertainty in arrival and delivery times.

While organisations can take steps to minimise project delivery uncertainty, organisations have to implement disincentives or incentives to better smooth demand otherwise, they face the risk of client abandonment, complaints and penalties. None of which is ideal for an organisation seeking to prosper and grow their market share.

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