Environmental Engineering Reference
In-Depth Information
approximation (PSFFA) by combining PSA and a fluid flow model to analyze sin-
gle server non-stationary queueing models. In their study, PSFFA was proved to
have better accuracy than PSA. However, PSFFA relies on invertible steady state
functions and therefore is not capable to analyze most multi-server non-stationary
queueing models. To address the issue of inverting complex queueing functions,
Chen et al. ( 2011a ) proposed an integration of the bisection method with PSFFA
(labeled B-PSFFA) for the multi-server non-stationary M ( t )/ E k ( t )/ c ( t ) queue.
B-PSFFA was used to analyze truck queues at marine container terminal gates
and compared to results from the model by Guan and Liu ( 2009 ). Simulation
results revealed that the stationary M / E k / c model is inaccurate, while the B-PSFFA
approximation can be highly accurate.
PSA, PSFFA, and B-PSFFA only consider truck queues at terminal gates,
and do not capture queues at the yard. To address both gate and yard truck
queues simultaneously, Chen et al. ( 2011b ) developed a two-layer queueing net-
work, in which the gate system is treated as multiple independent non-stationary
M ( t )/ M ( t )/1 queues (each gate lane is an M ( t )/ M ( t )/1 queue) and the yard system
as multiple independent non-stationary M ( t )/ G ( t )/1 queues (each yard zone is an
M ( t )/ G ( t )/1 queue). Truck flows from the gate to the yard are assumed to follow
a Poisson distribution, taking advantage of the ' equivalence property ' of M / M /1
system where the departure process of an M / M /1 queueing system with infinite
queueing capacity involves an Exponential distribution identical to the one of the
arrival process (Larson and Odoni 1981 ). This two-layer queueing network can
model truck queues at the gate and yard simultaneously. However, there are two
limitations: (a) the assumption that the gate service times follow an Exponential
distribution is not based on any empirical analysis; and (b) the assumption that a
gate system comprises of multiple independent queueing systems does not com-
ply with practice where a truck queue is served simultaneously by all gate lanes.
Ideally a gate system should be modeled as a multi-server queueing system.
The second part of the literature review focuses on truck arrival pattern opti-
mization studies. Huynh and Walton ( 2008 ) integrated a search heuristic with the
simulation model developed by Huynh et al. ( 2004 ) to reduce average truck turn
times to a target level specified by the terminal operator. This optimization model
has the disadvantage of long computational times due to an embedded simulation
model. Chen et al. ( 2011b ) compared computation times of a simple simulation
and a queueing model, and found that the simulation model is 122 times more
(computationally) expensive than the queueing model. As previously discussed,
Chen et al. ( 2011b ) developed a queueing network to model truck queues at the
gate and yard simultaneously. Furthermore, they integrated their queueing net-
work into an optimization model to minimize the weighted sum of three compo-
nents: (a) the quadratic deviation between the original arrival time and the shifted
arrival time of each truck, (b) queue length at the gate, and (c) queue length at
the yard. However, they did not describe how the weights of the three components
can be estimated to achieve optimal results. Furthermore, the first component of
the objective function may be difficult to calculate as, in practice, original truck
arrival times are not known during the planning phase. Nevertheless, to the best
of the authors' knowledge, Chen et al. ( 2011b ) is the only existing study modeling
Search WWH ::




Custom Search