A new, analysis-based, change of measure for tandem queues

In this paper, we introduce a simple analytical approximation for the overflow probability of a two-node tandem queue. From this, we derive a change of measure, which turns out to have good performance in almost the entire parameter space. The form of our new change of measure sheds an interesting new light on earlier changes of measure for the same problem, because here the transition zone from one measure to another - that they all have - arises naturally.\u

Alternative proof and interpretations for a recent state-dependent importance sampling scheme

Recently, a state-dependent change of measure for simulating overflows in the two-node tandem queue was proposed by Dupuis et al. (Ann. Appl. Probab. 17(4):1306–1346, 2007), together with a proof of its asymptotic optimality. In the present paper, we present an alternative, shorter and simpler proof. As a side result, we obtain interpretations for several of the quantities involved in the change of measure in terms of likelihood ratios

Tandem fluid queues fed by homogeneous on–off sources

We consider a tandem fluid model with multiple consecutive buffers. The input of buffer j+1 is the output from buffer j, while the first buffer is fed by a, possibly infinite, number of independent homogeneous on–off sources. The sources have exponentially distributed silent periods and generally distributed active periods. Under the assumption that the input rate of one source is larger than the maximum output rate of the first buffer, we are able to characterize the output from each buffer. Due to this fact we find (i) an equation for the Laplace–Stieltjes transform of the marginal content distribution of any buffer j2, (ii) explicit expressions for corresponding moments, and (iii) an explicit expression for the correlation between two buffer contents, again from the second buffer on. These results make use of a key observation concerning the aggregate contents of several consecutive buffers. For the case in which the active periods of the sources are exponential, the Laplace–Stieltjes transform is inverted. If there is only one source, all results are also valid for the first buffer

Mauvaise Conduite: Complicity and Respectability in the Occupied Nord, 1914-1918

For a two-node tandem fluid model with gradual input, we compute the joint steady-state buffer-content distribution. Our proof exploits martingale methods developed by Kella and Whitt. For the case of finite buffers, we use an insightful sample-path argument to extend an earlier proportionality result of Zwart to the network case

A comparison of random walks in dependent random environments

We provide exact computations for the drift of random walks in dependent random environments, including $k$-dependent and moving average environments. We show how the drift can be characterized and evaluated using Perron–Frobenius theory. Comparing random walks in various dependent environments, we demonstrate that their drifts can exhibit interesting behavior that depends significantly on the dependency structure of the random environment

Joint distributions for interacting fluid queues

Motivated by recent traffic control models in ATM systems, we analyse three closely related systems of fluid queues, each consisting of two consecutive reservoirs, in which the first reservoir is fed by a two-state (on and off) Markov source. The first system is an ordinary two-node fluid tandem queue. Hence the output of the first reservoir forms the input to the second one. The second system is dual to the first one, in the sense that the second reservoir accumulates fluid when the first reservoir is empty, and releases fluid otherwise. In these models both reservoirs have infinite capacities. The third model is similar to the second one, however the second reservoir is now finite. Furthermore, a feedback mechanism is active, such that the rates at which the first reservoir fills or depletes depend on the state (empty or nonempty) of the second reservoir.\ud The models are analysed by means of Markov processes and regenerative processes in combination with truncation, level crossing and other techniques. The extensive calculations were facilitated by the use of computer algebra. This approach leads to closed-form solutions to the steady-state joint distribution of the content of the two reservoirs in each of the models