Large closed queueing networks in semi-Markov environment and its application

The paper studies closed queueing networks containing a server station and $k$ client stations. The server station is an infinite server queueing system, and client stations are single-server queueing systems with autonomous service, i.e. every client station serves customers (units) only at random instants generated by a strictly stationary and ergodic sequence of random variables. The total number of units in the network is $N$. The expected times between departures in client stations are $(N\mu_j)^{-1}$. After a service completion in the server station, a unit is transmitted to the $j$th client station with probability $p_{j}$ $(j=1,2,...,k)$, and being processed in the $j$th client station, the unit returns to the server station. The network is assumed to be in a semi-Markov environment. A semi-Markov environment is defined by a finite or countable infinite Markov chain and by sequences of independent and identically distributed random variables. Then the routing probabilities $p_{j}$ $(j=1,2,...,k)$ and transmission rates (which are expressed via parameters of the network) depend on a Markov state of the environment. The paper studies the queue-length processes in client stations of this network and is aimed to the analysis of performance measures associated with this network. The questions risen in this paper have immediate relation to quality control of complex telecommunication networks, and the obtained results are expected to lead to the solutions to many practical problems of this area of research.Comment: 35 pages, 1 figure, 12pt, accepted: Acta Appl. Mat

Spectral properties of zero temperature dynamics in a model of a compacting granular column

The compacting of a column of grains has been studied using a one-dimensional Ising model with long range directed interactions in which down and up spins represent orientations of the grain having or not having an associated void. When the column is not shaken (zero 'temperature') the motion becomes highly constrained and under most circumstances we find that the generator of the stochastic dynamics assumes an unusual form: many eigenvalues become degenerate, but the associated multi-dimensional invariant spaces have but a single eigenvector. There is no spectral expansion and a Jordan form must be used. Many properties of the dynamics are established here analytically; some are not. General issues associated with the Jordan form are also taken up.Comment: 34 pages, 4 figures, 3 table

M/M/∞\infty queues in semi-Markovian random environment

In this paper we investigate an M/M/$\infty$ queue whose parameters depend on an external random environment that we assume to be a semi-Markovian process with finite state space. For this model we show a recursive formula that allows to compute all the factorial moments for the number of customers in the system in steady state. The used technique is based on the calculation of the raw moments of the measure of a bidimensional random set. Finally the case when the random environment has only two states is deeper analyzed. We obtain an explicit formula to compute the above mentioned factorial moments when at least one of the two states has sojourn time exponentially distributed.Comment: 17 pages, 2 figure

Campaigning against workplace ‘sexual harassment’ in the UK: Law, discourse and the news press c. 1975–2005

This article examines how and in what ways workplace ‘sexual harassment’ achieved social and legal recognition in the UK news press following its importation from North America in the mid-1970s. It assesses the role of feminist campaigners working within institutions (trade unions, human rights advocacy, the Equal Opportunities Commission and journalism itself) in shifting public discourse and in using the media to educate and promote social change. We demonstrate that the trajectory was far from a linear progression. Initial hostility within the popular press in the early 1980s was replaced with sympathetic coverage across the party-political spectrum by 1990. However, this consensus broke down in the 1990s as a result of politicised and polarised coverage of a series of claims brought by women in the services and armed forces against the backdrop of debates about ‘compensation culture’ and membership of the European Union. Whilst change was effected at the level of employment law, formal practice and in the human resources policies of larger employers, ‘sexual harassment myths’ were resilient as a thread within ‘everyday cultural discourse’ and, by implication, within informal workplace cultures

From Coordination to Stochastic Models of QoS

Reo is a channel-based coordination model whose operational semantics is given by Constraint Automata (CA). Quantitative Constraint Automata extend CA (and hence, Reo) with qua