Consider an aggregate arrival process A
N
obtained by multiplexing N on-off processes with exponential off periods of rate λ and subexponential on periods τon. As N goes to infinity, with λN → Λ, A
N
...approaches an M/G/∞ type process. Both for finite and infinite N, we obtain the asymptotic characterization of the arrival process activity period. Using these results we investigate a fluid queue with the limiting M/G/∞ arrival process A
t
∞ and capacity c. When on periods are regularly varying (with non-integer exponent), we derive a precise asymptotic behavior of the queue length random variable Q
t
P observed at the beginning of the arrival process activity periods
where ρ = A
t
∞ < c; r (c ≤ r) is the rate at which the fluid is arriving during an on period. The asymptotic (time average) queue distribution lower bound is obtained under more general assumptions regarding on periods than regular variation. In addition, we analyse a queueing system in which one on-off process, whose on period belongs to a subclass of subexponential distributions, is multiplexed with independent exponential processes with aggregate expected rate e
t
. This system is shown to be asymptotically equivalent to the same queueing system with the exponential arrival processes being replaced by their total mean value e
t
.
We provide a large deviation result for a random sum Nx n=0 X n , where N x is a renewal counting process and { X n } n 0 are i.i.d. random variables, independent of N x , with a common distribution ...that belongs to a class of square root insensitive distributions. Asymptotically, the tails of these distributions are heavier than e x and have zero relative decrease in intervals of length x , hence square root insensitive. Using this result we derive the asymptotic characterization of the busy period distribution in the stable GI/G/1 queue with square root insensitive service times; this characterization further implies that the tail behavior of the busy period exhibits a functional change for distributions that are lighter than e x .
We analyze the queueing behavior of long-tailed traffic flows under the Generalized Processor Sharing (GPS) discipline. We show a sharp dichotomy in qualitative behavior, depending on the relative ...values of the weight parameters. For certain weight combinations, an individual flow with long-tailed traffic characteristics is effectively served at a constant rate. The effective service rate may be interpreted as the maximum average traffic rate for the flow to be stable, which is only influenced by the traffic characteristics of the other flows through their average rates. In particular, the flow is essentially immune from excessive activity of flows with 'heavier'-tailed traffic characteristics. In many situations, the effective service rate is simply the link rate reduced by the aggregate average rate of the other flows. This confirms that GPS-based scheduling algorithms provide a potential mechanism for extracting significant multiplexing gains, while isolating individual flows. For other weight combinations however, a flow may be strongly affected by the activity of 'heavier'-tailed flows, and may inherit their traffic characteristics, causing induced burstiness. The stark contrast in qualitative behavior illustrates the crucial importance of the weight parameters. PUBLICATION ABSTRACT
We analyse a class of randomized Least Recently Used (LRU) cache replacement algorithms under the independent reference model with generalized Zipf's law request probabilities. The randomization was ...recently proposed for Web caching as a mechanism that discriminates between different document sizes. In particular, the cache maintains an ordered list of documents in the following way. When a document of size $s$ is requested and found in the cache, then with probability $p_s$ it is moved to the front of the cache; otherwise the cache stays unchanged. Similarly, if the requested document of size $s$ is not found in the cache, the algorithm places it with probability $p_s$ to the front of the cache or leaves the cache unchanged with the complementary probability $(1-p_s)$. The successive randomized decisions are independent and the corresponding success probabilities $p_s$ are completely determined by the size of the currently requested document. In the case of a replacement, the necessary number of documents that are least recently moved to the front of the cache are removed in order to accommodate the newly placed document. In this framework, we provide explicit asymptotic characterization of the cache fault probability. Using the derived result we prove that the asymptotic performance of this class of algorithms is optimized when the randomization probabilities are chosen to be inversely proportional to document sizes. In addition, for this optimized and easy-to-implement policy, we show that its performance is within a constant factor from the optimal static algorithm.
We consider a set of
N fluid On–Off flows that share a common server of capacity
c and a finite buffer
B. The server capacity is allocated using the generalized processor sharing scheduling ...discipline. Each flow has a minimum service rate guarantee that exceeds its long-term average demand
ρ
i
. The buffer sharing is unrestricted as long as there is available space. If the buffer is full, the necessary amount of fluid from the most demanding flows is discarded. When On periods are heavy-tailed, we show that the loss rate of a particular flow
i is asymptotically equal to the loss rate in a reduced system with capacity
c−∑
j≠
i
ρ
j
and buffer
B, where this flow is served in isolation. In particular, the system behaves as if it had
N times bigger buffer. This new insight on buffer multiplexing gain offers an additional tradeoff in distributing buffers between core and edge switching elements.
The economy in Serbia has not been working at its full capacity for a long time, which had left a great mark in economic stability of the country. The good side is that the environment pollution is ...less than in case of its full capacity. Therefore there shouldn't try to achieve the developed technologies at all costs, but it should orient to the utmost to agriculture and food production. Economically high developed countries pay a lot of attention to the healthy way of life and nutrition, and therefore the market, on which would sell the food products from Serbia, are with characteristic brand and undoubtable quality. Owing to the expressed trend for the healthy way of living, more and more people in high developed countries turn to aromatic and medicinal herbs which they use as spices, for therapeutic or medicinal purposes. Such trend shows also various industry branches, and they increasingly base their production on natural products. Hereof the aromatic and medicinal herbs start being more and more important economic resource of those countries which have them.
Ecology Today, Economy Tomorrow Jelenkovic, Predrag; Jelenkovic, Lilijana
Ekonomika, Journal for Economic Theory and Practice and Social Issues,
12/2012, Volume:
58, Issue:
4
Journal Article
Peer reviewed
Open access
The paper points out, first of all, the connections between ecology and economy, and their attitude towards environmental protection and global markets. In further development of the environment ...further major economic growth is understood. Three mutually determined factors are important for the significant economic growth: the sustainable economy, sustainable energy use and sustainable industrial activity. In today’s world the loss of natural resources is so much faster than any possibility of their restoration.The introduction of sustainability in the economy and ecology is very important issue not only for the present generation, but also for those to come.
Scalability of Wireless Networks Jelenkovic, P.R.; Momcilovic, P.; Squillante, M.S.
IEEE/ACM transactions on networking,
04/2007, Volume:
15, Issue:
2
Journal Article
Peer reviewed
This paper investigates the existence of scalable protocols that can achieve the capacity limit of c/radicN per source-destination pair in a large wireless network of N nodes when the buffer space of ...each node does not grow with the size of the network N. It is shown that there is no end-to-end protocol capable of carrying out the limiting throughput of c/radicN with nodes that have constant buffer space. In other words, this limit is achievable only with devices whose buffers grow with the size of the network. On the other hand, the paper establishes that there exists a protocol which realizes a slightly smaller throughput of c/radicNlogN when devices have constant buffer space. Furthermore, it is shown that the required buffer space can be very small, capable of storing just a few packets. This is particularly important for wireless sensor networks where devices have limited resources. Finally, from a mathematical perspective, the paper furthers our understanding of the difficult problem of analyzing large queueing networks with finite buffers for which, in general, no explicit solutions are available
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