Table 1 Arrival rates, service rates and... | Emerald Publishing

Table 1

Arrival rates, service rates and number of TAS-lanes and walk-in lanes considered

Definition	Description
Arrival rate for walk-in trucks (⁠ $λ_{2}$ ⁠)	1 to (⁠ $μ_{2}$ −1) trucks/hour
Arrival rate for TAS trucks (⁠ $λ_{1}$ ⁠)	1 to (⁠ $μ_{1}$ −1) trucks/hour*
Service rate for walk-in server (⁠ $μ_{2}$ ⁠)	5, 10, 15, 20, 25, 30 trucks/hour
Service rate for TAS server (⁠ $μ_{1}$ ⁠)	10, 15, 20, 25, 30, 35, 40, 45 trucks/hour*
Standard deviation of inter-arrival time for TAS trucks (⁠ $σ_{1 a}$ ⁠)	$\frac{2}{λ_{1}}, \frac{1}{λ_{1}}, \frac{1}{2 λ_{1}}$
Standard deviation of service time for TAS server (⁠ $σ_{1 s}$ ⁠)	$\frac{2}{μ_{1}}, \frac{1}{μ_{1}}, \frac{1}{2 μ_{1}}$
Standard deviation of inter-arrival time for walk-in trucks (⁠ $σ_{2 a}$ ⁠)	$\frac{2}{λ_{2}}, \frac{1}{λ_{2}}, \frac{1}{2 λ_{2}}$
Standard deviation of service time for TAS server (⁠ $σ_{1 s}$ ⁠)	$\frac{2}{μ_{2}}, \frac{1}{μ_{2}}, \frac{1}{2 μ_{2}}$
Number of walk-in lanes (⁠ $N_{1}$ ⁠)	1 to 2 lanes
Number of TAS-lanes (⁠ $N_{2}$ ⁠)	1 to 9 lanes

Definition	Description
Arrival rate for walk-in trucks ( $λ_{2}$ )	1 to ( $μ_{2}$ −1) trucks/hour
Arrival rate for TAS trucks ( $λ_{1}$ )	1 to ( $μ_{1}$ −1) trucks/hour*
Service rate for walk-in server ( $μ_{2}$ )	5, 10, 15, 20, 25, 30 trucks/hour
Service rate for TAS server ( $μ_{1}$ )	10, 15, 20, 25, 30, 35, 40, 45 trucks/hour*
Standard deviation of inter-arrival time for TAS trucks ( $σ_{1 a}$ )	$\frac{2}{λ_{1}}, \frac{1}{λ_{1}}, \frac{1}{2 λ_{1}}$
Standard deviation of service time for TAS server ( $σ_{1 s}$ )	$\frac{2}{μ_{1}}, \frac{1}{μ_{1}}, \frac{1}{2 μ_{1}}$
Standard deviation of inter-arrival time for walk-in trucks ( $σ_{2 a}$ )	$\frac{2}{λ_{2}}, \frac{1}{λ_{2}}, \frac{1}{2 λ_{2}}$
Standard deviation of service time for TAS server ( $σ_{1 s}$ )	$\frac{2}{μ_{2}}, \frac{1}{μ_{2}}, \frac{1}{2 μ_{2}}$
Number of walk-in lanes ( $N_{1}$ )	1 to 2 lanes
Number of TAS-lanes ( $N_{2}$ )	1 to 9 lanes

Note(s): * Values are based on data reported in the study of Guan and Liu (2009) and Huynh et al. (2011)