We consider the loss probability in the stationary M/G/1+G queue, i.e., the stationary M/G/1 queue with impatient customers whose impatience times are generally distributed. It is known that the loss probability is given in terms of the probability density function v(x) of the virtual waiting time and that v(x) is given by a formal series solution of a Volterra integral equation. In this paper, we show that the series solution of v(x) can be interpreted as the probability density function of a random sum of dependent random variables and we reveal its dependency structure through the analysis of a last-come first-served, preemptive-resume M/G/1 queue with workload-dependent loss. Furthermore, based on this observation, we show some properties of the loss probability.
Abstract We consider the loss probability P loss in the stationary M/G/1 queue with generally distributed impatience times (M/G/1+G queue). Recently, it was shown that P loss increases with service times in the convex order. In this paper, we show that P loss also increases with impatience times in the excess wealth order. With these results, we show that P loss in the M/D/1+D queue is smallest among all M/G/1+G queues with the same and finite arrival rate, mean service time, and mean impatience time.
We assessed muscarinic M1, M2 and M4 receptor subtypes in the hippocampus of Alzheimer’s and control brains by receptor autoradiography using ligands such as [125I]muscarinic toxin-1 ([125I]MT-1, M1 selective), [3H]AFDX-384 (M2 partially selective) and [125I]muscarinic toxin 4 ([125I]M4 toxin-1, M4 selective). Our results revealed a significant decrease in muscarinic M4 receptor binding in the dentate gyrus and CA4 regions of brain sections from Alzheimer’s patients compared to controls. No changes in the density of M1 or M2 receptor binding were observed. Our findings suggest that, relative to other muscarinic receptor subtypes, the M4 receptor could be the subtype which is selectively compromised in Alzeheimer’s disease (AD).
It is common practice to approximate the cell loss probability (CLP) of cells entering a finite buffer by the overflow probability (OVFL) of a corresponding infinite buffer queue, since the CLP is typically harder to estimate. We obtain exact asymptotic results for CLP and OVFL, for time-slotted queues where block arrivals in different time slots are i.i.d. and one cell is served per time slot. In this case the ratio of CLP to OVFL is asymptotically (1 - rho)/rho, where rho is the use or, equivalently, the mean arrival rate per time slot. Analogous asymptotic results are obtained for continuous time M/G/1 queues. In this case the ratio of CLP to OVFL is asymptotically 1 - rho.
The effect of the sampling position is investigated when measuring drip loss in porcine longissimus dorsi muscle. Measuring in biological tissue often includes an assumption of homogeneity of the muscle under investigation, an assumption that only applies to a certain extent. However, this assumption is particularly critical when measuring drip loss. In the present experiment two different methods for measuring drip loss were applied. The two methods use a considerably different sample size and thus a difference in sensitivity to the heterogeneity of the object to be measured may be expected. In other words, when measuring drip loss a large sample size may blur information about biological variations in the parameter under investigation. The influence of the sampling position on the drip loss measurement 34 pigs were selected from a random group of 204 pigs. The right and the left longissimus dorsi were excised and used as objects for measuring drip loss with two different methods. Each longissimus dorsi muscle was sliced in 11–15 slices of 2.5 cm thickness. The left longissimus dorsi was sampled in three positions for each slice and the drip loss was measured in each position applying the EZ-DripLoss method. The longissimus dorsi from the right side of the carcasses was measured with the bag method.
Many asymptotic results and numerical techniques have appeared in literature to evaluate the packet loss of GI/M/1/K queueing systems and some of them are applicable to heavy-tail distributed interarrival times. We have found a closed-form expression for the Laplace transform of Pareto probability distributions and it allows us to have a better setting to evaluate different performance measures of Pareto queueing systems. Particularly, in this paper we consider the evaluation of the asymptotic packet loss for the Pareto distributed interarrival times, i.e., Pareto/M/1/K queueing systems, through the use of the Pareto Laplace transform and its derivative
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