Fátima Ferreira

Assessment strategies for municipal selective waste collection schemes

An important strategy to promote a strong sustainable growth relies on an efficient municipal waste management, and phasing out waste landfilling through waste prevention and recycling emerges as a major target. For this purpose, effective collection schemes are required, in particular those regarding selective waste collection, pursuing a more efficient and high quality recycling of reusable materials. This paper addresses the assessment and benchmarking of selective collection schemes, relevant to guide future operational improvements. In particular, the assessment is based on the monitoring and statistical analysis of a core-set of performance indicators that highlights collection trends, complemented with a performance index that gathers a weighted linear combination of these indicators. This combined analysis underlines a potential tool to support decision makers involved in the process of selecting the collection scheme with best overall performance. The presented approach was applied to a case study conducted in Oporto Municipality, with data gathered from two distinct selective collection schemes.

Analysis of GI/M/s/c queues using uniformisation

We combine uniformisation, a powerful numerical technique for the analysis of continuous time Markov chains, with the Markov chain embedding technique to analyze GI/M/s/c queues. The main steps of the proposed approach are the computation of(1)the mixed-Poisson probabilities associated to the number of arrival epochs in the uniformising Poisson process between consecutive customer arrivals to the system; and (2)the conditional embedded uniformised transition probabilities of the number of customers in the queueing system immediately before customer arrivals to the system. To show the performance of the approach, we analyze queues with Pareto interarrival times using a stable recursion for the associated mixed-Poisson probabilities whose computation time is linear in the number of computed coefficients. The results for queues with Pareto interarrival times are compared with those obtained for queues with other interarrival time distributions, including exponential, Erlang, uniform and deterministic interarrival times. The obtained results show that much higher loss probabilities and mean waiting times in queue may be obtained for queues with Pareto interarrival times than for queues with the other mentioned interarrival time distributions, specially for small traffic intensities.

Simulation of semi-Markov processes and Markov chains ordered in level crossing

In this paper we address the simulation of stochastic processes ordered in level crossing, where, as proposed by Irle and Gani, X is slower in level crossing than Y if it takes X stochastically longer than Y to exceed any given level. This ordering has immediate applications to the analysis of first-passage times, which are important for detailed performance analysis of distributed computer and communication systems, like the response time of an Internet search-engine query. We provide algorithms for the simulation of level crossing ordered discrete time Markov chains, semi-Markov processes, and continuous time Markov chains under conditions derived recently.

Distribution of the Number of Losses in Busy-Periods of {M}^{X}/G/1/n Systems

This chapter addresses \({M}^{X}/G/1/n\) queues, i.e., single server batch Markovian arrival queues with finite customer waiting space of size n. Taking profit of the Markov regenerative structure of these systems, we develop an efficient recursive procedure to compute the probability mass function of the number of losses in busy-periods starting with an arbitrary number of customers in the system. The derived computational procedure is easy to implement and leads to a fast numerical computation of the loss probabilities. To illustrate the effectiveness of the procedure, loss probabilities are computed for a wide variety of queues, with different capacities, batch size distributions, and arrival and service parameters.

On the Blocking Probability and Loss Rates in Nonpreemptive Oscillating Queueing Systems

We analyze busy period related characteristics for oscillating systems, proposing a method to compute the mean length of busy periods for nonpreemptive oscillating \(M^ X/G/1/(n,a,b)\) systems. We further evaluate customer loss rates in busy cycles and the long-run blocking probability for such systems using the proposed method and earlier results from the authors for the mean number of customer losses in busy periods.

Stochastic ordering of semi-markov processes

In this tutorial we address the stochastic ordering of semi-Markov processes in the usual and level-crossing stochastic ordering senses. We highlight the sample-path approach for the comparison of semi-Markov processes and for the simulation of processes with a given distribution.

Level‐Crossing Ordering of M/M/c Retrial Queues

Using recent results of the authors for the level‐crossing ordering of Markov jump processes defined on a common partially ordered Polish space, we establish sufficient conditions for the level‐crossing ordering of two M/M/c retrial queues, written in terms of their usual parameterizations. As expected, these conditions are weaker than those required for the processes to be ordered in the usual stochastic ordering sense.

Some Results for GIX/M/s/c Queues

We address the time dependent and steady-state analysis of the number of customers in a GIX/M/s/c queuing system at prearrivals of batches. As a corollary, we derive the continuous time steady-state distribution of the number of customers in the system in continuous time. The obtained closed form solutions are easy to compute, as they involve only combinatorial calculations and mixed-Poisson probabilities or mixed-Poisson expected values. Finally, the steady-state distribution of the number of customers seen by customers at their arrival to the system, blocking probability and mean and variance of the waiting times in queue of non-blocked costumers are derived.