Obstetric operating room staffing and operating efficiency using queueing theory

Table 2 Results of queueing analysis for obstetric operating room events during peak hours (07:00 to 19:00)

Queue station	Obstetric operating room
λ	0.451
µ	0.865
Server Teams	2		3		4		5
P₀	0.479		0.479		0.479		0.479
Ls	0.552		0.524		0.521		0.521
Lq	0.031		0.003		0.000		0.000
Ws	1.225		1.162		1.157		1.156
Wq	0.069		0.006		0.001		0.000
Wq(0)	0.912		0.986 ^a		0.998 ^a		1.000
ρ (%)	0.261		0.174		0.130		0.104
*Steady-state distribution and operating characteristics*
*Server Teams*	2		3		4		5
	n	P_n	n	P_n	n	P_n	n	P_n
	0	0.478766	0	0.478766	0	0.478766	0	0.478766
	1	0.249549	1	0.249549	1	0.249549	1	0.249549
	2	0.065037	2	0.065037	2	0.065037	2	0.065037
	3	0.016950	3	0.011300	3	0.011300	3	0.011300
	4	0.004417	4 ^a	0.001963	4 ^a	0.001472	4	0.001472
	5	0.001151	5 ^a	0.000341	5 ^a	0.000192	5	0.000153
	6	0.000300	6	0.000059	6	0.000025	6	0.000016
	7	0.000078	7	0.000010	7	0.000003	7	0.000002
	8	0.000020	8	0.000002	8	< 0.000001	8	< 0.000001
	9	0.000005	9	< 0.000001
	10	0.000001
	11	< 0.000001

λ = arrival rate
µ = served rate
P₀ = probability that the system is empty
Ls = average number of people in the system
Lq = average length of the queue or the average number of people in a line waiting for service
Ws = average time for a patient in the system (waiting time plus service time)
Wq = average time spent in queue
Wq(0) = probability that the time spent in the queue is 0
ρ = utilization factor for entire system
n = number of patients in the system / number of operating rooms in use in the system
P_n = probability that n patients require simultaneous operating room service
^*Parameters at which Wq(0), n, and P_n are all optimized in that the probability of zero wait time is equal to or above 99% and probability that n patients requiring simultaneous operating room service is < 1%. At server team number 5, no further changes in P_n when n = 4 are noted, implying no added benefit to the system when server team number is 5

ISSN: 1472-6963