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Modeling Traffic Flow Interrupted by Incidents
 RUTGERS UNIVERSITY
, 2005
"... A steadystate M/M/C queueing system under batch service interruptions is introduced to model the traffic flow on a roadway link subject to incidents. When a traffic incident happens, either all lanes or part of a lane is closed to the traffic. As such, we model these interruptions either as comple ..."
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Cited by 8 (2 self)
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A steadystate M/M/C queueing system under batch service interruptions is introduced to model the traffic flow on a roadway link subject to incidents. When a traffic incident happens, either all lanes or part of a lane is closed to the traffic. As such, we model these interruptions either as complete service disruptions where none of the servers work or partial failures where servers work at a reduced service rate. We analyze this system in steady state and present a scheme to obtain the generating function of stationary number of vehicles on a link. For those links with large C values, the closedform solution of M/M/ ∞ queues under batch service interruptions can be used as an approximation. We present simulation results that show the validity of our approximate model.
HEAVYTRAFFIC LIMITS FOR MANYSERVER QUEUES WITH SERVICE INTERRUPTIONS
, 2008
"... We establish manyserver heavytraffic limits for G/M/n + M queueing models, allowing customer abandonment (the +M), subject to exogenous regenerative service interruptions. With unscaled service interruption times, we obtain a FWLLN for the queuelength process where the limit is an ordinary diffe ..."
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Cited by 7 (0 self)
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We establish manyserver heavytraffic limits for G/M/n + M queueing models, allowing customer abandonment (the +M), subject to exogenous regenerative service interruptions. With unscaled service interruption times, we obtain a FWLLN for the queuelength process where the limit is an ordinary differential equation in a twostate random environment. With asymptotically negligible service interruptions, we obtain a FCLT for the queuelength process, where the limit is characterized as the pathwise unique solution to a stochastic integral equation with jumps. When the arrivals are renewal and the interruption cycle time is exponential, the limit is a Markov process, being a jumpdiffusion process in the QED regime and an OU process driven by a Levy process in the ED regime (and for infiniteserver queues). A stochasticdecompostion property of the steadystate distribution of the limit process in the ED regime (and for infiniteserver queues) is obtained.
Journal of Statistics Education, v15n1: John A. Shanks file:///Users/williamnotz/Documents/JSE%20material/JSE%20Mar... Probability in Action: the Red Traffic Light
"... individuals, but it may not be republished in any medium without express written consent from the authors and advance notification of the editor. Key Words:Distributions; Modelling; Optimization; Problem solving; Emphasis on problem solving in mathematics has gained considerable attention in recent ..."
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individuals, but it may not be republished in any medium without express written consent from the authors and advance notification of the editor. Key Words:Distributions; Modelling; Optimization; Problem solving; Emphasis on problem solving in mathematics has gained considerable attention in recent years. While statistics teaching has always been problem driven, the same cannot be said for the teaching of probability where discrete examples involving coins and playing cards are often the norm. This article describes an application of simple probability distributions to a practical problem involving a car’s approach to a red traffic light, and draws on the ideas of density functions, expected value and conditional distributions. It provides a valuable exercise in applying theory in a practical context. 1.
Delay Estimation for Traffic Flow Interrupted by Incidents
"... Evaluation of the adverse impacts of traffic incidents on a highway network is a critical issue for an incident management program. In this paper, we present a delay estimation method to estimate delays caused by traffic incidents using a recently developed queueing based approach. We validate this ..."
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Evaluation of the adverse impacts of traffic incidents on a highway network is a critical issue for an incident management program. In this paper, we present a delay estimation method to estimate delays caused by traffic incidents using a recently developed queueing based approach. We validate this method by comparing its results with a simulation model.
M/M/ ∞ QUEUE WITH ONOFF SERVICE SPEEDS
"... In this paper we show the analysis of a special kind of M/M/ ∞ queueing system. We suppose that the rate of the servers alternates between two speeds according to an ONOFF process whose ON periods are exponentially distributed and with general OFF periods. We look at the particular case when the OF ..."
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In this paper we show the analysis of a special kind of M/M/ ∞ queueing system. We suppose that the rate of the servers alternates between two speeds according to an ONOFF process whose ON periods are exponentially distributed and with general OFF periods. We look at the particular case when the OFF service rate is zero while the distribution of the OFF periods is heavy tailed and for this case we derive the tail of the number of the customers in the system. An application of this model could be related to transportation systems where the M/M/ ∞ represents a delay line, s.a. a highway, whose crossing time may be unexpectedly interrupted, for a long time, by some accident. 1. Introduction and
M/M/ ∞ QUEUES IN SEMIMARKOVIAN RANDOM ENVIRONMENT
, 2008
"... Abstract. In this paper we investigate an M/M/ ∞ queue whose parameters depend on an external random environment that we assume to be a semiMarkovian process with finite state space. For this model we show a recursive formula that allows to compute all the factorial moments for the number of custom ..."
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Abstract. In this paper we investigate an M/M/ ∞ queue whose parameters depend on an external random environment that we assume to be a semiMarkovian process with finite state space. For this model we show a recursive formula that allows to compute all the factorial moments for the number of customers in the system in steady state. The used technique is based on the calculation of the raw moments of the measure of a bidimensional random set. Finally the case when the random environment has only two states is deeper analyzed. We obtain an explicit formula to compute the above mentioned factorial moments when at least one of the two states has sojourn time exponentially distributed. 1.
M/M/ ∞ QUEUES IN QUASIMARKOVIAN RANDOM ENVIRONMENT
, 2007
"... Abstract. In this paper we investigate an M/M/ ∞ queue whose parameters depend on an external random environment that we assume to be a quasiMarkovian process with finite state space. For this model we show a recursive formula that allows to compute all the factorial moments for the number of custo ..."
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Abstract. In this paper we investigate an M/M/ ∞ queue whose parameters depend on an external random environment that we assume to be a quasiMarkovian process with finite state space. For this model we show a recursive formula that allows to compute all the factorial moments for the number of customers in the system in steady state. The used technique is based on the calculation of the row moments of the area of a bidimensional random set. Finally some examples where it is possible to get explicit formulas are given together with comparisons with previous known results. 1.