Search Results (4)

An Erlang loss system, which is an $M/G/s/s$ queue, is a model used in various applications. In this paper, a controlled version of the process is defined. The objective is to maximize the expected time until the system is full when the service time is exponentially distributed. The control variable is the service rate. The dynamic programming equation satisfied by the value function F, from which the optimal control follows at once, is derived, and F is found explicitly when $s=2$ and $s=3$. The problem of minimising the probability of the system being saturated is also considered. Full article

Heterogeneous systems of limited capacity have general applications in manufacturing, but also in logistic or service systems due to the differences in server or workstation performance or work assignment; this is in close relationship with system flexibility, where saturation and blocking are ordinary situations of systems with high demand and limited capacity, and thus, accurate loss quantification is essential for performance evaluation. Multi-class systems of limited capacity have been studied much less than parallel homogeneous systems (Erlang models). In this context, accurate models for parallel heterogeneous ordered-entry systems were developed: without any prior queue, i.e., M/Mi/c/c, and with a k-capacity queue, i.e., M/Mi/c/c + k. These new matrix models gave an exact state formulation, and their accuracy was verified using discrete event simulation and comparison with literature results. Also, the effect of the queue capacity was studied in relationship to the pattern of service rates. Next, the heterogeneous recirculating system model was also developed with good approximation results. Finally, the proposed models were applied to evaluate systems with non-exponential service times using a new hybrid methodology by combining the Markovian model and the Monte Carlo method (MCM) for normal or lognormal service times, which also yielded useful good approximations to the simulated system. Full article

This paper considers a modified Erlang loss system for cognitive wireless networks and related applications. A primary user has pre-emptive priority over secondary users, and the primary customer is lost if upon arrival all the channels are used by other primary users. Secondary users cognitively use idle channels, and they can stay (either in an infinite buffer or in an orbit) in cases where idle channels are not available upon arrival or they are interrupted by primary users. While the infinite buffer model represents the case with zero sensing time, the infinite orbit model represents the case with positive sensing time. We obtain an explicit stability condition for the cases where arrival processes of primary users and secondary users follow Poisson processes, and their service times follow two distinct arbitrary distributions. The stability condition is insensitive to the service time distributions and implies the maximal throughout of secondary users. Moreover, we extend the stability analysis to the system with outgoing calls. For a special case of exponential service time distributions, we analyze the buffered system in depth to show the effect of parameters on the delay performance and the mean number of interruptions of secondary users. Our simulations for distributions rather than exponential reveal that the mean number of terminations for secondary users is less sensitive to the service time distribution of primary users. Full article

Purpose: Drugs with cardiovascular protective properties (statins, acetylsalicylic acid (ASS)) were assumed to have positive effects on patients suffering from glaucoma disease. The present retrospective study aimed to investigate the influence of statins, ASS or a combination of both on the glaucoma conversion and progression rate in glaucoma suspects and glaucoma patients with a 20-year follow-up period. Methods: A retrospective analysis of 199 eyes of 120 patients (63 male, 57 female) of the Erlanger Glaucoma Registry (EGR; ClinicalTrials.gov Identifier: NCT00494923; ISSN 2191-5008, CS-2011) was performed considering systemic therapy with statins, ASS or a combination of both: 107 eyes with ocular hypertension (OHT) and 92 eyes with pre-perimetric primary open-angle glaucoma (pre-POAG). All patients received an ophthalmological examination including morphometric and functional glaucoma diagnostics. Glaucoma conversion was defined as the conversion of OHT to pre-POAG. Glaucoma progression was defined as confirmed visual field loss. Data were shown as percentages. Statistical analysis was performed by Chi-Quadrat tests. Results: 1. Glaucoma conversion/progression was observed in 46.7% of the subjects, additionally in combination with hypercholesterinemia in 76.8%. 2. Statins: 27.3% of eyes under systemic statin therapy showed a conversion/progression. Patients taking statins ≥ 10 years yielded a reduced conversion/progression rate (p = 0.028, non-significant after Bonferroni–Holm). 3. ASS: 34.7% of eyes under systemic ASS therapy showed a conversion/progression. A significantly lower conversion/progression rate was observed after ASS therapy ≥ 12 years (p = 0.017, significant after Bonferroni–Holm). 4. ASS and statins: 25.0% of eyes under combined therapy showed a conversion/progression. A significantly reduced conversion/progression rate was reached after 8 years of combined therapy (p = 0.049, non-significant after Bonferroni–Holm). Conclusions: Patients with ocular hypertension and early glaucoma seem to benefit from adjuvant cardiovascular protective therapy. However, the benefits and disadvantages of treatment with statins and/or ASS should be kept in mind. Thus, a thorough risk–benefit evaluation has to be performed for each patient individually to avoid unwanted side effects. Full article