5,253 research outputs found
Analysis of operating characteristics for the heterogeneous batch arrival queue with server startup and breakdowns
In this paper we consider a like-queue production system in which server startup
and breakdowns are possible. The server is turned on (i.e. begins startup)
when N units are accumulated in the system and off when the system is empty.
We model this system by an M[x]/M/1 queue with
server breakdowns and startup time under the N policy. The arrival rate varies according to the server's status:
off, startup, busy, or breakdown.
While the server is working, he is subject to
breakdowns according to a Poisson process. When the server breaks down, he requires repair
at a repair facility, where the repair time follows the negative exponential distribution.
We study the steady-state behaviour of the system size distribution at
stationary point of time as well as the queue size distribution at departure point of time
and obtain some useful results.
The total expected cost function per unit time is developed to determine the optimal operating
policy at a minimum cost. This paper provides the minimum expected cost and the optimal operating
policy based on assumed numerical values of the system parameters. Sensitivity analysis is also provided
Propagation of epistemic uncertainty in queueing models with unreliable server using chaos expansions
In this paper, we develop a numerical approach based on Chaos expansions to
analyze the sensitivity and the propagation of epistemic uncertainty through a
queueing systems with breakdowns. Here, the quantity of interest is the
stationary distribution of the model, which is a function of uncertain
parameters. Polynomial chaos provide an efficient alternative to more
traditional Monte Carlo simulations for modelling the propagation of
uncertainty arising from those parameters. Furthermore, Polynomial chaos
expansion affords a natural framework for computing Sobol' indices. Such
indices give reliable information on the relative importance of each uncertain
entry parameters. Numerical results show the benefit of using Polynomial Chaos
over standard Monte-Carlo simulations, when considering statistical moments and
Sobol' indices as output quantities
Ramp metering and freeway bottleneck capacity
The objective of this study is to determine whether ramp meters increase the capacity of active freeway bottlenecks, and if they do, how. The traffic flow characteristics at twenty-seven active bottlenecks in the Twin Cities have been studied for seven weeks without ramp metering and seven weeks with ramp metering. A series of hypotheses regarding the relationships between ramp metering and the capacity of active bottlenecks are developed and tested against empirical traffic data. It is found that meters increase the bottleneck capacity by postponing and sometimes eliminating bottleneck activations (a 73 percent increase in the duration of the pre-queue transition period), accommodating higher (2 percent) flows during the pre-queue transition period, and increasing queue discharge flow rates after breakdown (3 percent). The two-capacity hypothesis about flow drops after breakdown was also examined and results strongly suggest the percentage flow drops at various bottlenecks follow a normal distribution (mean 5.5 percent, standard deviation 2.3 percent). The implications of these findings on the design of efficient ramp control strategies are discussed, as well as future research directions.transportation, travel behavior, congestion, ramp meters
AN QUEUE WITH OPTIONAL SERVICE AND WORKING BREAKDOWN
In this study, a batch arrival single service queue with two stages of service (second stage is optional) and working breakdown is investigated. When the system is in operation, it may breakdown at any time. During breakdown period, instead of terminating the service totally, it continues at a slower rate. We find the time-dependent probability generating functions in terms of their Laplace transforms and derive explicitly the corresponding steady state results. Furthermore, numerous measures indicating system performances, such as the average queue size and the average queue waiting time, has been obtained. Some of the numerical results and graphical representations were also presented
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