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Table 5 The best fitting results of queueing network for Events A and B

From: Could we employ the queueing theory to improve efficiency during future mass causality incidents?

Event

A

B

Queue Stationb

Triage

Assess12a

Assess34a

X-ray

CTa

Tre1a

Tre2a

Consult

Triage

Assess12a

Assess34a

X-ray

Tre1a

Tre2a

Consult

λ

41

5

35.99

31

9.01

7.99

33.01

41

22

16.85

5.15

8.89

4.68

17.32

22

μ

15

4

6

20

10

6

6

12

6

6

12

20

2

1

12

Servers

3

2

7

2

1

2

6

4

4

3

1

1

3

18

2

L s

11.31

2.05

9.68

3.88

9.15

2.39

14.12

7.50

12.71

15.75

0.75

0.80

4.52

38.25

11.48

L q

8.58

0.80

3.68

2.33

8.24

1.06

8.62

4.08

9.04

12.95

0.32

0.36

2.18

20.93

9.64

Ws (hour)

0.28

0.41

0.27

0.13

1.01

0.30

0.43

0.18

0.58

0.93

0.15

0.09

0.97

2.21

0.52

Wq (hour)

0.21

0.16

0.10

0.07

0.91

0.13

0.26

0.10

0.41

0.77

0.06

0.04

0.47

1.21

0.44

ρ (%)

91.11

62.53

85.71

77.50

90.14

66.60

91.69

85.42

91.67

93.62

42.90

44.47

77.79

96.22

91.67

  1. aAssess12: assessment for triage 1 and 2. Assess34: assessment for triage 3 and 4. CT computed tomography scan. Tre1: Treatment 1. Tre2: Treatment 2
  2. bλ the arrival rate, µ the served rate, Ls Average number of people in the system, Lq Average length of the queue or the average number of people in a line awaiting service, Ws Average time for a customer in the system (waiting time plus service time), Wq Average waiting time or the average length of time that a customer waits before being served, ρ utilization factor for the system