We consider n independent points with a common but arbitrary density fin R a. Two points (X~, Xj) are joined by an edge when a certain set S(X~, Xj) does not contain any other data points. The expected number E(N) of edges in the graph depends upon n, f and the definition of S. Examples include rectangles, spheres and loons; these lead to the graph of all dominance pairs, the Gabriel graph and ...

This paper examines several simple algorithms for routing packets on butterry networks with bounded queues. We show that for any greedy queuing protocol, a routing problem in which each of the N inputs sends a packet to a randomly chosen output requires O(log N) steps, with high probability, provided that the queue size is a suuciently large, but xed, constant. We also show that for any determi...

We examine the properties of a promising new traac descriptor for ATM networks, namely the entropy of cell streams. The entropy is a measure of the disorganization among cells within a traac stream; alternatively we can say that entropy captures the amount of randomness in cell scattering. We study the entropy of ON-OFF sources with respect to the typical queue parameters of interest: average q...

In order to deliver assured Quality of Service (QoS) to the customer in terms of minimizing the expected waiting time in the queue; the service providers are putting a lot of effort. The varying calling pattern of the customers during different times of the day poses many challenging problems in terms of allocating the number of employees in an efficient manner to handle the customer’s calls. T...

We consider a feedback finite fluid queue with downward jumps, where the net flow rate and the jump size for the fluid are controlled by a background Markov chain with a finite state space. The finite means that the fluid queue has a finite buffer. The feedback means that the transition structure of the background process may change when the buffer content becomes empty or full. In this paper, ...

We consider single-server queues with exponentially distributed service times, in which the arrival process is governed by a semi-Markov process (SMP). Two service disciplines, processor sharing (PS) and random service (RS), are investigated. We note that the sojourn time distribution of a type-l customer who, upon his arrival, meets k customers already present in the SMP/M/1/PS queue is identi...

Heilbronn’s triangle problem asks for the least ∆ such that n points lying in the unit disc necessarily contain a triangle of area at most ∆. Heilbronn initially conjectured ∆ = O(1/n). As a result of concerted mathematical effort it is currently known that there are positive constants c and C such that c logn/n ≤ ∆ ≤ C/n for every constant ǫ > 0. We resolve Heilbronn’s problem in the expected ...

This paper examines several simple algorithms for routing packets on butterfly networks with bounded queues. We show that for any greedy queuing protocol, a routing problem in which each of the N inputs sends a packet to a randomly chosen output requires O(logN) steps, with high probability, provided that the queue size is a sufficiently large, but fixed, constant. We also show that for any det...

ABSTRACT We analyze a single server queue with modified Bernoulli server vacations based on exhaustive service. Unlike other vacation policies, we assume that only at the completion of service of the last customer in the system, the server has the option to take a vacation or to remain idle in the system waiting for the next customer to arrive. The service times of the customers have been assum...

A congestion avoidance scheme allows a network to operate in the region of low delay and high throughput. Such scheme prevent a network from entering in to congested state. RED(Random Early Detection), is one such congestion avoidance mechanism used for effectively control of congestion. In RED, router uses only the average queue size, as a congestion indicator and the average queue length is i...