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Equation 1 Using Queueing Theory to Determine Operating Room Staffing Needs. Tucker, James; Barone, James; Cecere, Joseph; Blabey, Robert; Rha, Chan-Kook Journal of Trauma-Injury Infection & Critical Care. 46(1):71-79, January 1999. Equation 1 © 1999 Lippincott Williams & Wilkins, Inc. Published by Lippincott Williams & Wilkins, Inc. 2

Equation 2 Using Queueing Theory to Determine Operating Room Staffing Needs. Tucker, James; Barone, James; Cecere, Joseph; Blabey, Robert; Rha, Chan-Kook Journal of Trauma-Injury Infection & Critical Care. 46(1):71-79, January 1999. Equation 2 © 1999 Lippincott Williams & Wilkins, Inc. Published by Lippincott Williams & Wilkins, Inc. 3

Equation 3 Using Queueing Theory to Determine Operating Room Staffing Needs. Tucker, James; Barone, James; Cecere, Joseph; Blabey, Robert; Rha, Chan-Kook Journal of Trauma-Injury Infection & Critical Care. 46(1):71-79, January 1999. Equation 3 © 1999 Lippincott Williams & Wilkins, Inc. Published by Lippincott Williams & Wilkins, Inc. 4

Equation 4 Using Queueing Theory to Determine Operating Room Staffing Needs. Tucker, James; Barone, James; Cecere, Joseph; Blabey, Robert; Rha, Chan-Kook Journal of Trauma-Injury Infection & Critical Care. 46(1):71-79, January 1999. Equation 4 © 1999 Lippincott Williams & Wilkins, Inc. Published by Lippincott Williams & Wilkins, Inc. 5

Equation 5 Using Queueing Theory to Determine Operating Room Staffing Needs. Tucker, James; Barone, James; Cecere, Joseph; Blabey, Robert; Rha, Chan-Kook Journal of Trauma-Injury Infection & Critical Care. 46(1):71-79, January 1999. Equation 5 © 1999 Lippincott Williams & Wilkins, Inc. Published by Lippincott Williams & Wilkins, Inc. 6

Equation 6 Using Queueing Theory to Determine Operating Room Staffing Needs. Tucker, James; Barone, James; Cecere, Joseph; Blabey, Robert; Rha, Chan-Kook Journal of Trauma-Injury Infection & Critical Care. 46(1):71-79, January 1999. Equation 6 © 1999 Lippincott Williams & Wilkins, Inc. Published by Lippincott Williams & Wilkins, Inc. 7

Equation 7 Using Queueing Theory to Determine Operating Room Staffing Needs. Tucker, James; Barone, James; Cecere, Joseph; Blabey, Robert; Rha, Chan-Kook Journal of Trauma-Injury Infection & Critical Care. 46(1):71-79, January 1999. Equation 7 © 1999 Lippincott Williams & Wilkins, Inc. Published by Lippincott Williams & Wilkins, Inc. 8

Equation 8 Using Queueing Theory to Determine Operating Room Staffing Needs. Tucker, James; Barone, James; Cecere, Joseph; Blabey, Robert; Rha, Chan-Kook Journal of Trauma-Injury Infection & Critical Care. 46(1):71-79, January 1999. Equation 8 © 1999 Lippincott Williams & Wilkins, Inc. Published by Lippincott Williams & Wilkins, Inc. 9

Equation 9 Using Queueing Theory to Determine Operating Room Staffing Needs. Tucker, James; Barone, James; Cecere, Joseph; Blabey, Robert; Rha, Chan-Kook Journal of Trauma-Injury Infection & Critical Care. 46(1):71-79, January 1999. Equation 9 © 1999 Lippincott Williams & Wilkins, Inc. Published by Lippincott Williams & Wilkins, Inc. 10

Equation 10 Using Queueing Theory to Determine Operating Room Staffing Needs. Tucker, James; Barone, James; Cecere, Joseph; Blabey, Robert; Rha, Chan-Kook Journal of Trauma-Injury Infection & Critical Care. 46(1):71-79, January 1999. Equation 10 © 1999 Lippincott Williams & Wilkins, Inc. Published by Lippincott Williams & Wilkins, Inc. 11

Equation 11 Using Queueing Theory to Determine Operating Room Staffing Needs. Tucker, James; Barone, James; Cecere, Joseph; Blabey, Robert; Rha, Chan-Kook Journal of Trauma-Injury Infection & Critical Care. 46(1):71-79, January 1999. Equation 11 © 1999 Lippincott Williams & Wilkins, Inc. Published by Lippincott Williams & Wilkins, Inc. 12

Table 1 Using Queueing Theory to Determine Operating Room Staffing Needs. Tucker, James; Barone, James; Cecere, Joseph; Blabey, Robert; Rha, Chan-Kook Journal of Trauma-Injury Infection & Critical Care. 46(1):71-79, January 1999. Table 1 . Comparison of the queueing model with simulation in analyzing the likelihood of two or more OR cases occurring simultaneously during the night shift © 1999 Lippincott Williams & Wilkins, Inc. Published by Lippincott Williams & Wilkins, Inc. 13

Figure 1 Using Queueing Theory to Determine Operating Room Staffing Needs. Tucker, James; Barone, James; Cecere, Joseph; Blabey, Robert; Rha, Chan-Kook Journal of Trauma-Injury Infection & Critical Care. 46(1):71-79, January 1999. Figure 1 . Probability distribution of patient arrivals compared with that predicted if the cases are exponentially distributed. There is similarity but not an exact match. © 1999 Lippincott Williams & Wilkins, Inc. Published by Lippincott Williams & Wilkins, Inc. 14

Figure 2 Using Queueing Theory to Determine Operating Room Staffing Needs. Tucker, James; Barone, James; Cecere, Joseph; Blabey, Robert; Rha, Chan-Kook Journal of Trauma-Injury Infection & Critical Care. 46(1):71-79, January 1999. Figure 2 . Distribution of lengths of OR cases for the 62 patients studied. The distribution reflects the necessary Poisson pattern. © 1999 Lippincott Williams & Wilkins, Inc. Published by Lippincott Williams & Wilkins, Inc. 15

Figure 3 Using Queueing Theory to Determine Operating Room Staffing Needs. Tucker, James; Barone, James; Cecere, Joseph; Blabey, Robert; Rha, Chan-Kook Journal of Trauma-Injury Infection & Critical Care. 46(1):71-79, January 1999. Figure 3 . Probability of two or more patients needing the operating room simultaneously at any time based on an average night case length of 80.79 minutes per year and the number of night cases seen per year. © 1999 Lippincott Williams & Wilkins, Inc. Published by Lippincott Williams & Wilkins, Inc. 16

Table 2 Using Queueing Theory to Determine Operating Room Staffing Needs. Tucker, James; Barone, James; Cecere, Joseph; Blabey, Robert; Rha, Chan-Kook Journal of Trauma-Injury Infection & Critical Care. 46(1):71-79, January 1999. Table 2 . Probability table © 1999 Lippincott Williams & Wilkins, Inc. Published by Lippincott Williams & Wilkins, Inc. 17

Figure 4 Using Queueing Theory to Determine Operating Room Staffing Needs. Tucker, James; Barone, James; Cecere, Joseph; Blabey, Robert; Rha, Chan-Kook Journal of Trauma-Injury Infection & Critical Care. 46(1):71-79, January 1999. Figure 4 . Percentage chance of an institution, with an average case length of 80.79 minutes per patient and various numbers of night patients per year, having two or more patients needing the operating room sometime during the year. © 1999 Lippincott Williams & Wilkins, Inc. Published by Lippincott Williams & Wilkins, Inc. 18

Table 3 Using Queueing Theory to Determine Operating Room Staffing Needs. Tucker, James; Barone, James; Cecere, Joseph; Blabey, Robert; Rha, Chan-Kook Journal of Trauma-Injury Infection & Critical Care. 46(1):71-79, January 1999. Table 3 . Probability of a second case when presented with a first case of a specific length based on the number of nighttime cases per year at any institution © 1999 Lippincott Williams & Wilkins, Inc. Published by Lippincott Williams & Wilkins, Inc. 19