Index Policies for Optimal Mean-Variance Trade-Off of Inter-delivery Times in Real-Time Sensor Networks

A problem of much current practical interest is the replacement of the wiring infrastructure connecting approximately 200 sensor and actuator nodes in automobiles by an access point. This is motivated by the considerable savings in automobile weight, simplification of manufacturability, and future upgradability. A key issue is how to schedule the nodes on the shared access point so as to provide regular packet delivery. In this and other similar applications, the mean of the inter-delivery times of packets, i.e., throughput, is not sufficient to guarantee service-regularity. The time-averaged variance of the inter-delivery times of packets is also an important metric. So motivated, we consider a wireless network where an Access Point schedules real-time generated packets to nodes over a fading wireless channel. We are interested in designing simple policies which achieve optimal mean-variance tradeoff in interdelivery times of packets by minimizing the sum of time-averaged means and variances over all clients. Our goal is to explore the full range of the Pareto frontier of all weighted linear combinations of mean and variance so that one can fully exploit the design possibilities. We transform this problem into a Markov decision process and show that the problem of choosing which node's packet to transmit in each slot can be formulated as a bandit problem. We establish that this problem is indexable and explicitly derive the Whittle indices. The resulting Index policy is optimal in certain cases. We also provide upper and lower bounds on the cost for any policy. Extensive simulations show that Index policies perform better than previously proposed policies

Pathwise Performance of Debt Based Policies for Wireless Networks with Hard Delay Constraints

Hou et al have introduced a framework to serve clients over wireless channels when there are hard deadline constraints along with a minimum delivery ratio for each client's flow. Policies based on "debt," called maximum debt first policies (MDF) were introduced, and shown to be throughput optimal. By "throughput optimality" it is meant that if there exists a policy that fulfils a set of clients with a given vector of delivery ratios and a vector of channel reliabilities, then the MDF policy will also fulfill them. The debt of a user is the difference between the number of packets that should have been delivered so as to meet the delivery ratio and the number of packets that have been delivered for that client. The maximum debt first (MDF) prioritizes the clients in decreasing order of debts at the beginning of every period. Note that a throughput optimal policy only guarantees that \begin{small} \liminf_{T \to \infty} \frac{1}{T}\sum_{t=1}^{T} \mathbbm{1}\{\{client n$'s packet is delivered in frame$t} \} \geq q_{i} \end{small}, where the right hand side is the required delivery ratio for client $i$. Thus, it only guarantees that the debts of each user are $o(T)$, and can be otherwise arbitrarily large. This raises the interesting question about what is the growth rate of the debts under the MDF policy. We show the optimality of MDF policy in the case when the channel reliabilities of all users are same, and obtain performance bounds for the general case. For the performance bound we obtain the almost sure bounds on $\limsup_{t\to\infty}\frac{d_{i}(t)}{\phi(t)}$ for all $i$, where $\phi(t) = \sqrt{2t\log\log t}$

Trends in the profile of non hodgkins lymphoma in North and South India: a study from two tertiary care hospitals in India

Background: A number of environmental and chemical factors have been thought to been implicated in the occurrence of Non-Hodgkin’s Lymphomas (NHLs).To fill the knowledge gap in various aspect of the disease, this study was undertaken at this tertiary care centre in Delhi and Bangalore.Methods: This was a prospective observational study conducted in two defenses medical centre in India among patients of Non Hodgkins Lymphoma, registered at Command hospital Airforce Bangalore and Army Hospital (Research and Referral), New Delhi, between March 2016 and March 2019.Results: The disease showed a bimodal onset in both centres with 26 (26%) and 24 (24%) cases occurring in the age group of 31-40 years and 24 (24%) and 25 (25%) cases occurring in the age group of >60 years at CHAF (B) and AH (RR) respectively. B cell Lymphoma was the most common type of NHL seen in 85% and 89% patients, whereas T-cell lymphomas constituted 13% and 11% at CHAF (B) and AH (RR).  32(32%) patients presented with an Ann Arbor Stage 1 or 2 disease whereas 68(68%) patients were with Stage 3 or 4 disease at both the centers. IPI score was ≥3 in 45 % and 43% patients.Conclusions: NHL in India is a homogeneous and uniform disease. But there was increased detection of hepatosplenomegaly and associated hepatitis B/C in the southern part of India. Also, the occurrence of Cutaneous T cell lymphoma was only seen in the south India centre. The early stage NHLs has better survival and increase chance of complete response