### Browsing by Author "Tsoucas, P."

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Item Concavity of Throughput in Series of Queues with Finite Buffers.(1989) Anantharam, Venkat; Tsoucas, P.; ISRConcavity of the output process with respect to buffer size is established in a series of DOT/M/1/B queues with loss at the first node. Similarly, one shows concavity of the throughput with respect to the number of servers and the buffer sizes in a node belonging to a series of DOT/M/s/B queues.Item Monotonicity of Throughput in Non-Markovian Networks.(1988) Tsoucas, P.; Walrand, J.; ISRMonotonicity of throughput is established in some non-Markovian queueing networks by means of path-wise comparisons. In a series of DOT/GI/s/N queues with loss at the first node it is proved that increasing the waiting room and/or the number of servers increases the throughput. For a closed network of DOT/GI/s queues it is shown that the throughput increases as the total number of jobs increases. The technique used for these results does not apply to blocking systems with finite buffers and feedback. Using a stronger coupling argument we prove throughput monotonicity as a function of buffer size for a series of two DOT/M/1/N queues with loss and feedback from the second to the first node.Item Ode and Diffusion Limits in Large Symmetric Circuit Switched Networks.(1989) Tsoucas, P.; ISRThis paper considers a large symmetric star-shaped circuit- switched network where each route requires one circuit from each of two links. Interarrival and holding times of calls are exponential. The process of the number of free circuits in each link is analyzed. An ordinary differential equation limit is established along with a diffusion approximation limit conjectured by Whitt [Wh].Item A Proof of the Markov Chain Tree Theorem.(1988) Anantharam, Venkat; Tsoucas, P.; ISRLet X be a finite set, P a stochastic matrix on X, and P{BAR} = lim{AS n GOES TO x} (1/n){SIGMA k=0 to n-1, P^k}. Let G = (X, E) be the weighted directed graph on X associated to P, with weights P_ij. An arborescence is a subset a {IS AN ELEMENT OF} E which has at most one edge out of every node, contains no cycles, and has maximum possible cardinality. The weight of an arborescence is the product of its edge weights. Let A denote the set of all arborescences. Let A_ij denote the set of all arborescences which have j as a root and in which there is a directed path from i to j. Let ||A||, resp. ||A_ij||, be the sum of the weights of the arborescences in A, resp. A_ij. The Markov chain tree theorem states that p_ij = ||A_i,j||/||A||. We give a proof of this theorem which is probabilitistic in nature.Item Stochastic Monotonicity of the Output Process of Parallel Queues.(1989) Tsoucas, P.; ISRThis paper considers the output process of a system of K DOT /M/I queues in parallel with Bernoulli routing of jobs upon arrival. It is shown that the output process is stochastically increasing as the routing probabilities approach 1/K in a certain sense. The proof crucially depends on the fact that the absolute value of a simple random walk is a time-homogeneous birth and death process.Item Transient Behavior of Circuit-Switched Networks.(1989) Panier, E.; Tsoucas, P.; ISRThis paper is concerned with strong approximation in queueing networks. A model of a circuit-switched network with fixed routes is considered in the limiting regime where the link capacities and the offered traffic are increased at the same rate. The process of normalized queue lengths is shown to converge almost surely to a sliding mode solution of an ordinary differential equation. The solution is shown to possess a unique stable point. It is reached exponentially fast or in finite time, depending on the values of the parameters. This has implications on the settling time of the network. The technique is applicable to closed Jackson networks and their settling times. In contrast with other asymptotic results on queueing networks it does not make use of product form distributions and extends easily to non- Markovian models.