Harrison, J.M. (1985). Brownian Motion and Stochastic Flow Systems. Wiley, New York. Home/Search Document Not in Database Summary Related Articles Check |
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The Complexity Of Optimal Queuing Network Control - Christos Papadimitriou And (Correct)
....problem can be solved byaningeniously simple index calculation [Git] and an optimal policy corresponds to prioritizing the different classes bysorting their respectiveindices. Due to the difficulty of the problem, researchinthis area has been deflected to approaches suchasdiffusion approximations [Har] and certain other rigorous approximation algorithms [BPT,KK] In this paper we prove that the problem of finding an optimal control policy in a multiclass closedqueuing network is an intractable problem.Nobodywas really expecting an efficient algorithm for this problem, at least in this ....
J. M. Harrison, Brownian Motion and Stochastic Flow Systems, Prentice Hall, 1985.
Optimal Risk/Dividend Distribution Control Models. Applications.. - Taksar (1999) (Correct)
....respect to F t , V (X ) Gamma V (x) oe(X t )V (X t )dW t Gamma (V (X t ) Gamma V (X t Gamma ) In particular V (X ) 9.1) V (X t ) Gamma V (X t Gamma ) The proof of this theorem can be found in [47] p. 301 or [31] Ch.4. 9.2. Skorohod problem on a real line. Let (x) and oe(x) be Lipschitz continuous functions. Let u 2 R be fixed. A solution to the Skorohod problem in ( Gamma1; u] with initial position x is a pair (X t ; L t ) of cadlag F t adapted processes, such that L t is nonnegative and increasing ....
....both X and L have a discontinuity at 0 if x u. Existence and uniqueness of a solution to the Skorohod problem in a much more general setting is proved in [42] In the case of oe(x) and (x) being constants, the solution to the Skorohod problem (9.2) 9. 4) can be written in a closed form (see [31] Ch.2) L t = maxfmax st (x s oeW s Gamma u) 0g; 9.5) X t = x t oeW t Gamma L t : 9.6) ....
Harrison, J.M. (1985). Brownian Motion and Stochastic Flow Systems. Wiley, New York.
A Min-Plus System Theory for Constrained Traffic.. - Chang, Cruz, Le.. (2002) (2 citations) (Correct)
.... As q(t) A 1 (t) B(t) A(t) C(t) I(t) L(t) 18 the work conserving link with a nite bu er solves the so called Skorokhod re ection problem with two boundaries [29] where A(t) C(t) is the free process, I(t) is the lower boundary process, and L(t) is the upper boundary process (see e.g. [19, 18] for more detailed discussions of the re ection problem) Since the work conserving with a nite bu er also solves the bu erconstrained trac regulation problem, it follows from (24) that the upper boundary process of the re ection problem admits the following close form representation (in terms of ....
J. M. Harrison, Brownian Motion and Stochastic Flow Systems, New-York, Wiley, 1985.
Convexity Properties of Loss and Overflow Functions - Kumaran, Mandjes, Stolyar (2001) (Correct)
.... ct h[q(0) f; c; b] t) g[q(0) f; c; b] t) 1) where the lower and upper regulations h and g are unique non decreasing continuous functions such that A b 0 q(t) b; t 0; B b h(0) g(0) 0; 2 C b Ifq(s) 0gdh(s) 0; t 0; and D b Ifq(s) bgdg(s) 0; t 0; see Harrison [5], Proposition 2.4.6. The functions h and g we will also refer to as the (cumulative) idleness and (cumulative) loss function, respectively. In case of an infinite buffer, b = 1, the queue length is defined similarly: q(t) q(0) f(t) ct h[q(0) f; c] t) 2) A1 0 q(t) t 0; B1 h(0) ....
....respectively. In case of an infinite buffer, b = 1, the queue length is defined similarly: q(t) q(0) f(t) ct h[q(0) f; c] t) 2) A1 0 q(t) t 0; B1 h(0) 0; C1 Ifq(s) 0gdh(s) 0; t 0: In addition, for infinite buffer the expression for the idleness h is explicit (see [5], Proposition 2.2.3) h(t) inf (q(0) f(s) cs) 0] where denotes the minimum of two numbers. Note that, for any t 0, q(t) is monotone non decreasing on the initial condition q(0) The following two simple lemmas are needed to prove the key Lemma 2.3 below. Lemma 2.1 Let q 1 ; q ....
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J.M. Harrison. Brownian Motion and Stochastic Flow Systems. Wiley, 1985.
In Search of Sensitivity in Network Optimization - Chen, Pandit, Meyn (2003) (Correct)
....lead to intractable optimality equations for all but the simplest network models. This has led to the development of various alternative network models tuned to address particular issues such as optimal control in heavy tra#c ; the impact of breakdowns; or steady state performance (e.g. [20, 13, 3, 19, 49, 11, 32]. The simplest model is the linear, deterministic fluid model used in, for example, 2, 10, 9, 14, 34, 35, 36, 45, 52, 50] It provides a framework for policy synthesis for large networks based on linear programming methods, and this leads to attractive approaches to sensitivity analysis through ....
....optimal for the stochastic network model, provided a certain e#ective cost is monotone [43, Theorems 4.3 4.5] The deterministic fluid model can be refined by the addition of an additive disturbance. When the disturbance is Gaussian then one obtains the Brownian model developed in, for example, [46, 20, 47, 21, 33, 37, 24, 20, 29, 11, 32]. Certain small Brownian network models have yielded to exact analysis, and a translation of the optimal policy to a network model with general statistics is then shown to be approximately optimal by comparison with the Brownian network. A now standard approach to policy translation is to impose ....
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J. M. Harrison. Brownian Motion and Stochastic Flow Systems. Wiley, New York, NY, 1985.
Strategic Entry and Market Leadership in a.. - Shackleton.. (2002) (Correct)
....is at P 0 . Define the stopping time T j T j = inf 0 : P t as the first time that P reaches P starting from P 0 . Since the future evolution of P is unknown, time T j is essentially a random variable measuring the time firm j will be active. Using equation (1. 11) in Harrison [9] and an application of a simple change in variables, the cumulative distribution function of the first passage time T j can be written as: Pr [T j t] # #t # # t # # # t # (19) where #, # as in (11) and # ( is the standard normal cumulative distribution function. ....
M. J. Harrison. Brownian Motion and Stochastic Flow Systems. Robert E. Krieger Publishing Company, 1985.
Moderate Deviations for Queues with Long-Range Dependent Input - Chang, Yao, Zajic (1996) (1 citation) (Correct)
....the state process of a queue with input Y and a deterministic service mechanism that depletes work at rate c. In queueing literature, V (t) is often referred to as the virtual waiting time process, or the workload inventory process. See, for instance, Chang [3] Dueld and O Connell [11] Harrison [14], and Sigman and Yao [22] among others. Let V (t) V (nt) n; in particular, V (1) V (n) n. Theorem 4.1 The process fV (n) n; n 0g satis es the LDP with speed and good rate function V ( IR 7 IR, V ( 2 inf ; 1.19) for some 0. ....
J.M. Harrison, Brownian Motion and Stochastic Flow Systems. Wiley, New York, 1985.
Lyapunov Method for the Stability of Fluid Networks - Ye, Chen (2000) (Correct)
....also a fluid solution. Proof. First, it can be checked directly that (Q(t) T (t) satisfies (7) 9) To verify (10) it is su#cient to prove that, I j (t) 0 if k#C(j) Q k (t) 0. It can be proven by using the continuity of the one dimensional reflection mapping (see for example Harrison [21]) however, we include a more direct proof here. Suppose U j (t) k#C(j) Q k (t) 0 for some station index j. Then, there exist #, # 0, such that U j (s) 2# for any s #, t #] Since U k#C(j) Q U j (u.o.c. there exists N, for any n N , we have U U j (s) # on ....
Harrison, J.M. (1985). Brownian motion and Stochastic Flow Systems. Wiley, New York.
Optimal Risk/Dividend Distribution Control Models. Applications.. - Taksar (1999) (Correct)
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Harrison, J.M. (1985). Brownian Motion and Stochastic Flow Systems. Wiley, New York.
A Theory of Deterministic Queuing Systems for the Internet - Le Boudec, Thiran (2003) (2 citations) (Correct)
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J. M. Harrison. Brownian Motion and Stochastic Flow Systems. Wiley, New-York, 1985.
Estimating Tail Probabilities in Queues via Extremal Statistics - Glynn, Zeevi (1999) (Correct)
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M.J. Harrison. Brownian Motion and Stochastic Flow Systems. Wiley, NY, 1985.
Network Characteristics: Modelling, Measurements and.. - Gunawardena, Key.. (Correct)
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M. Harrison, Brownian Motion and Stochastic Flow Systems, John Wiley and Sons, New York, 1985.
In Search of Sensitivity in Network Optimization - Chen, Pandit, Meyn (2003) (Correct)
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J.M. Harrison, Brownian Motion and Stochastic Flow Systems (Wiley, New York, 1985).
Optimal Pricing and Replenishment in a Single-Product.. - Chen, Wu, Yao (2004) (Correct)
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Harrison, J.M. 1985. Brownian Motion and Stochastic Flow Systems, Wiley, New York.
Estimating Tail Decay for Stationary Sequences via Extreme Values - Zeevi, Glynn (2001) (Correct)
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J.M. Harrison. Brownian Motion and Stochastic Flow Systems. Wiley, NY, 1985.
Properties of the reflected Ornstein-Uhlenbeck process - Ward, Glynn (2002) (Correct)
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Harrison, J. M.: 1985, Brownian Motion and Stochastic Flow Systems. New York: John Wiley & Sons.
Regulating Functions on Partially Ordered Sets - Venkat Anantharam Takis (2002) (Correct)
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Harrison, J.M. (1985) Brownian Motion and Stochastic Flow Systems. Wiley, New York.
NETWORK CALCULUS Parts II and III - A Theory of.. - Le Boudec, Thiran (2004) (Correct)
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J. M. Harrison. Brownian Motion and Stochastic Flow Systems. Wiley, New-York, 1985.
A Diffusion Approximation for Markovian Queue with Reneging - Ward, Glynn (2002) (Correct)
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Harrison, J. M.: 1985, Brownian Motion and Stochastic Flow Systems. New York: John Wiley & Sons.
A Min,+ System Theory for Constrained Traffic.. - Chang, Cruz, Le.. (2002) (Correct)
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J. M. Harrison, Brownian Motion and Stochastic Flow Systems.New York: Wiley, 1985.
Large Deviations, Moderate Deviations, and Queues with.. - Chang, Yao, Zajic (1997) (Correct)
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J.M. Harrison, Brownian Motion and Stochastic Flow Systems. Wiley, New York, 1985.
Rc 20649 (91385) 12/5/96 - Computer Science Mathematics (Correct)
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J. M. Harrison. Brownian motion and stochastic flow systems. Wiley, New York, 1985.
Extension of the PAC Framework to Finite and Countable Markov.. - Gamarnik (2002) (5 citations) (Correct)
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Heavy Traffic Limits for Queues with Many Deterministic .. - Jelenkovic.. (Correct)
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A Probabilistic Analysis - Ramudhin, Bartholdi, III, Calvin.. (2003) (Correct)
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Harrison M. 1985. Brownian Motion and Stochastic Flow Systems, John Wiley & Sons.
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