Waiting-Time Asymptotics for the M/G/2 Queue with Heterogeneous Servers

In this paper, we consider a c-server queuing model in which customers arrive according to a batch Markovian arrival process (BMAP). These customers are served in groups of varying sizes ranging from a predetermined value L through a maximum size, K. The service times are exponentially distributed. Any customer not entering into service immediately orbit in an infinite space. These orbiting customers compete for service by sending out signals that are exponentially distributed with parameter . Under a full access policy freed servers offer services to orbiting customers in groups of varying sizes. This multi-server retrial queue under the full access policy is a QBD process and the steady state analysis of the model is performed by exploiting the structure of the coefficient matrices. Some interesting numerical examples are discussed.     

Wiener-Hopf analysis of an M/G/1 queue with negative customers and of a related class of random walks

Two variants of an M/G/1 queue with negative customers lead to the study of a random walkX _n+1=[X _n + _n ]⁺ where the integer-valued _n are not bounded from below or from above, and are distributed differently in the interior of the state-space and on the boundary. Their generating functions are assumed to be rational. We give a simple closed-form formula for , corresponding to a representation of the data which is suitable for the queueing model. Alternative representations and derivations are discussed. With this formula, we calculate the queue length generating function of an M/G/1 queue with negative customers, in which the negative customers can remove ordinary customers only at the end of a service. If the service is exponential, the arbitrarytime queue length distribution is a mixture of two geometrical distributions.Supported by the European grant BRA-QMIPS of CEC DG XIII.     

Optimization of headspace solid-phase microextraction gas chromatography-atomic emission detection analysis of monomethylmercury

Optimum conditions for headspace solid-phase microextraction (HS-SPME) in the analysis of monomethylmercury (MeHg) have been determined. Sodium tetra(n-)propylborate (NaBPr(4)) is used as derivatization reagent to promote volatility. A simple aluminium bar was used to cool the SPME fiber to about 2 degrees C during the equilibration phase just before extraction. HS-SPME was performed using different fibers. The 100 microm polydimethylsiloxane (PDMS) and 65 microm polydimethylsiloxane-divinylbenzene (PDMS-DVB) fibers showed the best results. Although the extraction efficiency for MeHg derivative of the polydimethylsiloxane-Carboxen (PDMS-CAR) fiber is similar to the other fibers, desorption of MeHg derivative from a PDMS-CAR fiber is poor. Factors affecting the HS-SPME process such as adsorption and desorption times, ionic strength (salting-out) and extraction temperature have been evaluated and optimized thoroughly. The highest extraction efficiency for the PDMS fiber was obtained by extraction at a low temperature (2 degrees C) immediately after equilibration at 30 degrees C. With the PDMS-DVB and PDMS-CAR fiber improvement of extraction efficiency at lower temperatures is negligible. Repeated extraction out of the same vial revealed that about 30% of MeHg derivative is extracted from the headspace with a PDMS fiber at 2 degrees C and about 70% with a PDMS-DVB fiber. Repeated extraction with two different fiber coatings showed that the PDMS-CAR fiber also extracts about 70% but that the desorption is incomplete. Attempts to improve the desorption failed due to degradation of the MeHg derivate at high injection temperatures. The limit of detection (3sigma) was 16 pg/L MeHg. The relative standard deviation (n = 8) for 100 pg/L of MeHg was found to be 5%. Linearity of the HS-SPME-GC-atomic emission detection method was established over at least two orders of magnitude in the range 0-2000 pg/L. Recovery of a surface water sample spiked at 2 ng/L was 85%. The suitability of the procedure was demonstrated by analysis of a surface water sample that showed a concentration of 100 pg/L MeHg. The optimized method can be used with standard commercial equipment without further adaptations.     

Non-Kinetic Effects Convolute Activity and Tafel Analysis for the Alkaline Oxygen Evolution Reaction on NiFeOOH Electrocatalysts

A large variety of nickel-based catalysts has been investigated for the oxygen evolution reaction (OER) in alkaline media. However, their reported activity, as well as Tafel slope values, vary greatly. To understand this variation, we studied electrodeposited Ni₈₀Fe₂₀OOH catalysts with different loadings at varying rotation rates, hydroxide concentrations, with or without sonication. We show that, at low current density (<5 mA cm⁻²), the Tafel slope value is ≈30 mV dec⁻¹ for Ni₈₀Fe₂₀OOH. At higher polarization, the Tafel slope continuously increases and is dependent on rotation rate, loading, hydroxide concentration and sonication. These Tafel slope values are convoluted by non-kinetic effects, such as bubbles, potential-dependent changes in ohmic resistance and (internal) OH⁻ gradients. As best practise, we suggest that Tafel slopes should be plotted vs. current or potential. In such a plot, it can be appreciated if there is a kinetic Tafel slope or if the observed Tafel slope is influenced by non-kinetic effects.     

Queue-length balance equations in multiclass multiserver queues and their generalizations

A classical result for the steady-state queue-length distribution of single-class queueing systems is the following: The distribution of the queue length just before an arrival epoch equals the distribution of the queue length just after a departure epoch. The constraint for this result to be valid is that arrivals, and also service completions, with probability one occur individually, i.e., not in batches. We show that it is easy to write down somewhat similar balance equations for multidimensional queue-length processes for a quite general network of multiclass multiserver queues. We formally derive those balance equations under a general framework. They are called distributional relationships and are obtained for any external arrival process and state-dependent routing as long as certain stationarity conditions are satisfied and external arrivals and service completions do not simultaneously occur. We demonstrate the use of these balance equations, in combination with PASTA, by (1) providing very simple derivations of some known results for polling systems and (2) obtaining new results for some queueing systems with priorities. We also extend the distributional relationships for a nonstationary framework.     

Performance analysis of polling systems with retrials and glue periods

We consider gated polling systems with two special features: (i) retrials and (ii) glue or reservation periods. When a type-i customer arrives, or retries, during a glue period of the station i, it will be served in the following service period of that station. Customers arriving at station i in any other period join the orbit of that station and will retry after an exponentially distributed time. Such polling systems can be used to study the performance of certain switches in optical communication systems. When the glue periods are exponentially distributed, we obtain equations for the joint generating functions of the number of customers in each station. We also present an algorithm to obtain the moments of the number of customers in each station. When the glue periods are generally distributed, we consider the distribution of the total workload in the system, using it to derive a pseudo-conservation law which in turn is used to obtain accurate approximations of the individual mean waiting times. We also investigate the problem of choosing the lengths of the glue periods, under a constraint on the total glue period per cycle, so as to minimize a weighted sum of the mean waiting times.     

Asymptotic behaviour of the tandem queueing system with identical service times at both queues

Consider a tandem queue consisting of two single-server queues in series, with a Poisson arrival process at the first queue and arbitrarily distributed service times, which for any customer are identical in both queues. For this tandem queue, we relate the tail behaviour of the sojourn time distribution and the workload distribution at the second queue to that of the (residual) service time distribution. As a by-result, we prove that both the sojourn time distribution and the workload distribution at the second queue are regularly varying at infinity of index 1−ν, if the service time distribution is regularly varying at infinity of index −ν (ν>1). Furthermore, in the latter case we derive a heavy-traffic limit theorem for the sojourn time S ⁽²⁾ at the second queue when the traffic load ρ↑ 1. It states that, for a particular contraction factor Δ (ρ), the contracted sojourn time Δ (ρ) S ⁽²⁾ converges in distribution to the limit distribution H(·) as ρ↑ 1 where .     

Polling: past,present, and perspective

This is a survey on polling systems, focussing on the basic single-server multi-queue polling system in which the server visits the queues in cyclic order. The main goals of the paper are: (i) to discuss a number of the key methodologies in analyzing polling models; (ii) to give an overview of recent polling developments; and (iii) to present a number of challenging open problems.     

Stability results for stochastic delayed recurrent neural networks with discrete and distributed delays

We present new conditions for asymptotic stability and exponential stability of a class of stochastic recurrent neural networks with discrete and distributed time varying delays. Our approach is based on the method using fixed point theory, which do not resort to any Liapunov function or Liapunov functional. Our results neither require the boundedness, monotonicity and differentiability of the activation functions nor differentiability of the time varying delays. In particular, a class of neural networks without stochastic perturbations is also considered. Examples are given to illustrate our main results.