Constant Service Time Model

Instructions: You can use this Constant Service Time Model, by providing the arrival rate per time period \((\lambda)\), and the constant service rate per time period \((\mu)\), using the form below:

Arrival Rate per time period \((\lambda)\) =
Constant Service Rate per time period \((\mu)\) =
Time period unit =

Constant Service Time Model Calculator

More about the Constant Service Time Model for you to have a better understanding of what this calculator will provide you.

The Constant Service Time Model (or usually known as M/D/1 server discipline) is similar to the Single Server Model (or usually known as M/M/1 server discipline), with the main difference that for the Constant Service Time Model, the service times are constant.

Constant Service Time Model Calculator

What are the main parameters calculated for this waiting line model?

The main parameters of a waiting line of this type, and actually for most queuing theory models, are:

\[ \text{Average Number of Units in the Queue } = L_q = \frac{\lambda^2}{2\mu(\mu - \lambda)}\] \[ \text{Average Time a unit spend in the Queue } = W_q = \frac{\lambda}{2\mu (\mu - \lambda)}\] \[ \text{Average Number of Units in the System } = L_s = L_q \frac{\lambda}{\mu}\] \[ \text{Average Time a unit spend in the System } = W_s = W_q + \frac{1}{\mu}\]

These shown above are queuing formula, but be careful that they apply specifically for the constant service time assumption.

Constant Service Time

More Waiting Line Models

Other common waiting line models are the single-server model or the multiple server model , M/M/s, and as we go making different assumptions about number of lines, servers and channels, we can arrive to fairly complex waiting line models.

One example with more complex assumption is the case of the single period model, also known as the newsboy problem. .

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