this paper, we consider a queueing model of a single-hop network with randomly changing connectivity and we study the effect of varying connectivity on the performance of the system. The queueing model consists of a single server and N parallel queues (Fig. 1). The time is slotted. At slot t each queue i may be either connected to the server or not; that is denoted by the binary variable Ci(t), which is equal to 1 and 0 respectively. It is called the connectivity variable of queue i. The connectivity varies randomly with time. There are Manuscript received August 20, 1991; revised February 24, 1992. This work was presented in part at the IEEE International Symposium on Information Theory, Budapest, Hungary, June 24-28, 1991. L. Tassiulas is with the Department of Electrical Engineering, Polytechnic University, 6 Metrotech Center, Brooklyn, NY 11201. A. Ephremides is with the Department of Electrical Engineering, University of Maryland, College Park, MD 20742. IEEE Log Number 9204101. cffO ........ a I a 2 Fig. 1. Single-hop network with time varying connectivity. Solid line between a queue and the server denotes that the queue is connected to the server (it may receive service). Dashed line denotes that the queue is disconnected

Shortest Path Problems are among the most studied network flow optimization problems, with interesting applications in various fields. One such field is transportation, where shortest path problems of different kinds need to be solved. Due to the nature of the application, transportation scientists need very flexible and efficient shortest path procedures, both from the running time point of view, and also for the memory requirements. Since no "best" algorithm currently exists for every kind of transportation problem, research in this field has recently moved to the design and implementation of "ad hoc" shortest path procedures, which are able to capture the peculiarities of the problems under consideration. The aim of this work is to present in a unifying framework both the main algorithmic approaches that have been proposed in the past years for solving the shortest path problems arising most frequently in the transportation field, and also some important implementation techniques ...

We investigate the minimum weight path problem in networks whose link weights and link delays are both functions of time. We demonstrate that in general there exist cases in which no finite path is optimal leading us to define an infinite path (naturally, containing loops) in such a way that the minimum weight problem always has a solution. We also characterize the structure of an infinite optimal path. In many practical cases, finite optimal paths do exist. We formulate a criterion that guarantees the existence of a finite optimal path and develop an algorithm to find such a path. Some special cases, e.g., optimal loopless paths, are also discussed.

Portable devices have more data storage and increasing communication capabilities everyday. In addition to classic infrastructure based communication, these devices can exploit human mobility and opportunistic contacts to communicate. We analyze the characteristics of such opportunistic forwarding paths. We establish that opportunistic mobile networks in general are characterized by a small diameter, a destination device is reachable using only a small number of relays under tight delay constraint. This property is first demonstrated analytically on a family of mobile networks which follow a random graph process. We then establish the validity of this result empirically with four data sets capturing human mobility, using a new methodology to efficiently compute all the paths that impact the diameter of an opportunistic mobile networks. We complete our analysis of network diameter by studying the impact of intensity of contact rate and contact duration. This work is, to our knowledge, the first validation that the so called “small world ” phenomenon applies very generally to opportunistic networking between mobile nodes. 1.

In this paper, we study dynamic shortest path problems, which is to determine a shortest path from a specified source node to every other node in the network where arc travel times change dynamically. We consider two problems: the minimum time walk problem (which is to find a walk with the minimum travel time) and the minimum cost walk problem (which is to find a walk with the minimum travel cost). The minimum time walk problem is known to be polynomially solvable for a class of networks called FIFO networks. This paper makes the following contributions: (i) we show that the minimum cost walk problem is an NP-complete problem; (ii) we develop a pseudopolynomial-time algorithm to solve the minimum cost walk problem (for integer travel times); and (iii) we develop a polynomial-time algorithm for the minimum time walk problem arising in road networks with traffic lights.

We consider the problem of trave ling with least expec ted dela y in networ ks whose link delays change probabilistically acc ording to Markov cha ins. This is a typical routing problem in dynamic computer communication networ ks. We formulate sever al optimization problems, posed on infinite and finite horizons, and consider them with and without using memory in the decision making proc ess. We prove that all these problems ar e, in genera l, intrac table. Howe ver, for networks with nodal stochastic delays, a simple polynomial optimal solution is prese nted. This is typical of high-spee d networks, in which the dominant delays are incurre d by the nodes. For more gene ral networks, a tracta ble ε-optimal solution is pre sented.

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We consider two approaches that model timetable information in public transportation systems as shortest-path problems in weighted graphs. In the time-expanded approach, every event at a station, e.g., the departure of a train, is modeled as a node in the graph, while in the timedependent approach the graph contains only one node per station. Both approaches have been recently considered for (a simplified version of) the earliest arrival problem, but little is known about their relative performance. Thus far, there are only theoretical arguments in favor of the time-dependent approach. In this paper, we provide the first extensive experimental comparison of the two approaches. Using several real-world data sets, we evaluate the performance of the basic models and of several new extensions towards realistic modeling. Furthermore, new insights on solving bicriteria optimization problems in both models are presented. The time-expanded approach turns out to be more robust for modeling more complex scenarios, whereas the time-dependent approach shows a clearly better performance.

This paper proposes and solves the Time-Interval All Fastest Path (allFP) query. Given a user-defined leaving or arrival time interval I, a source node s and an end node e, allFP asks for a set of all fastest paths from s to e, one for each sub-interval of I. Note that the query algorithm should find a partitioning of I into sub-intervals. Existing methods can only be used to solve a very special case of the problem, when the leaving time is a single time instant. A straightforward solution to the allFP query is to run existing methods many times, once for every time instant in I. This paper proposes a solution based on novel extensions to the A * algorithm. Instead of expanding the network many times, we expand once. The travel time on a path is kept as a function of leaving time. Methods to combine travel-time functions are provided to expand a path. A novel lower-bound estimator for travel time is proposed. Performance results reveal that our method is more efficient and more accurate than the discrete-time approach. 1

Algorithms for route planning in transportation networks have recently undergone a rapid development, leading to methods that are up to three million times faster than Dijkstra’s algorithm. We give an overview of the techniques enabling this development and point out frontiers of ongoing research on more challenging variants of the problem that include dynamically changing networks, time-dependent routing, and flexible objective functions.