In this paper we treat the general version of the semi-Markov storage model, introduced first by Senturia and Puri: transitions in the state of the system occur at a discrete sequence of time points, described by a two-state semi-Markov process. An input occurs at an instant of transition to state 1 and a demand for release occurs at an instant of transition to state 2. Assuming general distributions for all the variables involved, we show that the dam contents just after the nth input converges properly in distribution as n →∞ under conditions of stability; likewise that after the nth demand. We also show that the demand lost due to shortage of stock, accumulated over instants of demand as well as over time, obeys a strong law and a central limit theorem.

Let Un be the time between the nth and (n + 1)th arrivals to a single-server queuing system, and Vn the nth arrival's service time. There are quite a few models in which {Un, Vn, n ≥ 1} is a regenerative sequence. In this paper, some light and heavy traffic limit theorems are proved solely under this assumption; some of the light traffic results, and all the heavy traffic results, are new for two such models treated earlier by the author; and all the results are new for the semi-Markov queuing model.In the last three sections, the results are applied to a single-server queue whose input is the output of a G/G/1 queue functioning in light traffic.

Let Un be the time between the nth and (n + 1)th arrivals to a single-server queuing system, and Vn the nth arrival's service time. There are quite a few models in which {Un, Vn , n ≥ 1} is a regenerative sequence. In this paper, some light and heavy traffic limit theorems are proved solely under this assumption; some of the light traffic results, and all the heavy traffic results, are new for two such models treated earlier by the author; and all the results are new for the semi-Markov queuing model. In the last three sections, the results are applied to a single-server queue whose input is the output of a G/G/1 queue functioning in light traffic.

Background: In pediatric daycare surgery, I gel has been used safely and effectively in anesthetized children. I-gel size is determined routinely by the manufacture's recommended weight-based method. The dimension of thenar eminence can help in determining I-gel size. The aim of this study was to compare the weight-based method and thenar eminence dimension method in the selection of I gel. Subjects and Methods: The prospective, randomized, single-blind study included 80 patients of the age group 6 months to 12 years, the American Society of Anesthesiologists class I, II, and III of either gender who were undergoing surgery under general anesthesia. Group 1– (n = 40) recommended weight-based method and group 2 – (n = 40) thenar eminence-based method. Parameters observed were proper placement, adequate ventilation, leak fraction (LF), and number of attempts. Results: Proper placement and adequate ventilation were comparable between two groups. LF is statistically higher in group 1 compared to group 2 (P = 0.003). The mean insertion time was 17 s in each group. The number of attempts, hemodynamic parameters, and ease of insertion were all comparable between two groups. Conclusions: Thenar eminence dimension can be the better method for the recommended weight-based method, especially in the emergency situations when the weight cannot be determined.

In this paper we treat the general version of the semi-Markov storage model, introduced first by Senturia and Puri: transitions in the state of the system occur at a discrete sequence of time points, described by a two-state semi-Markov process. An input occurs at an instant of transition to state 1 and a demand for release occurs at an instant of transition to state 2.Assuming general distributions for all the variables involved, we show that the dam contents just after the nth input converges properly in distribution as n →∞ under conditions of stability; likewise that after the nth demand. We also show that the demand lost due to shortage of stock, accumulated over instants of demand as well as over time, obeys a strong law and a central limit theorem.