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of passenger service, and the queuing mechanism is based on first come, first served basis Extensive research has been carried out in recent years to determine mathematical formulations which adequately represent the processing system [2, 10, 14, 19, 21, 53, 56] Because of the variability associated with passenger behavior at an airport, it is virtually impossible to obtain precise mathematical formulations for delay at processors However, reasonable estimates of delay and corresponding queue lengths are possible using simple formulations One such formulation [17, 35, 52, 56] is that of a multiple station queuing system with a Poisson arrival distribution and a service time distribution which is characterized by the average service time and the variance of the average service time as shown in Eq (10-1) 2 + t2 Ws = 2t 2 k t k +1
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n= k 1
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(10-1)
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where Ws = average delay per person = average demand rate t = average service time for a processor, the reciprocal of the average service rate of a processor, = standard deviation of the average service time of a processor k = number of processors n = counter in the equation This equation is valid when the average demand rate on the system of processors is less than to total service rate of the processors, k ; that is, the ratio of the average demand rate to the total service rate is less than 1 When the number of processors k is equal to 1, this equation reduces to 2 + t2 Ws = (10-2) t 2 2 ( ) or since is equal to /k 2 + t2 Ws = t 2 2 (1 )
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(10-3)
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For a single server system which exhibits a Poisson arrival distribution and an exponential service time distribution, Eq (10-1) reduces to Ws = or Ws = ( ) (1 )
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(10-4)
(10-5)
Airport Design
For a single server system which exhibits a Poisson arrival distribution and a constant service time distribution, Eq (10-1) reduces to Ws = or Ws = 2 (1 ) 2 ( )
(10-6)
(10-7)
When demand is less than capacity, the following expression gives the average line length N over the period being analyzed and consists of those in service and those waiting for service at a processor 1 N = Ws +
(10-8)
When > 1 there is statistical delay plus excess delay which is defined by a deterministic model For design purposes it is sufficient to estimate delays in such a system in which the statistical delay Ws is computed from the appropriate equation above with = 090 and the excess delay We is added to this from the equation below to compute total processor delay The rationale for computing the statistical delay with = 09 is that in reality as demand approached capacity the delay cannot become infinite as airline or airport operating practices will limit delay by utilizing additional servers We = T ( k ) 2 k
(10-9)
where We = delay when the demand exceeds the service rate T = time period during which the demand exceeds the service rate = total demand on the system of processors k = number of processors = service rate of a processor It is usually assumed that the time required to reduce the demand to capacity T is about one-half of the time period being analyzed Typically when demand exceeds capacity, the operator of the facility will increase the number of operating service facilities to alleviate the growth in both waiting time and queue lengths However, the extent to which this is done is a function of airline operating policies and the availability of additional manpower and physical facilities The average line length over the period analyzed N including those in service and those waiting for service; when demand exceeds, capacity can be estimated by the following equation 1 N = Ws + W e +
(10-10)
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