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. . The main parameters of a waiting line of this type are:

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

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.

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