Sharif Digital Repository

We consider an M/M/1 queueing system with inventory under the (r,Q) policy and with lost sales, in which demands occur according to a Poisson process and service times are exponentially distributed. All arriving customers during stockout are lost. We derive the stationary distributions of the joint queue length (number of customers in the system) and on-hand inventory when lead times are random variables and can take various distributions. The derived stationary distributions are used to formulate long-run average performance measures and cost functions in some numerical examples  

Partially-observed network data collected by link-tracing based sampling methods is often being studied to obtain the characteristics of a large complex network. However, little attention has been paid to sampling from directed networks such as WWW and Peer-to-Peer networks. In this paper, we propose a novel two-step (sampling/estimation) framework to measure nodal characteristics which can be defined by an average target function in an arbitrary directed network. To this end, we propose a personalized PageRank-based algorithm to visit and sample nodes. This algorithm only uses already visited nodes as local information without any prior knowledge about the latent structure of the network.... 

We provide an analytical investigation of the entanglement dynamics for a system composed of an arbitrary number of qubits dissipating into a common environment. Specifically, we consider product initial states with a given number of excitations whose evolution remains confined on low-dimensional subspaces of the operators space. We then find for which pairs of qubits entanglement can be generated and can persist at a steady state. Finally, we determine the stationary distribution of entanglement as well as its scaling versus the total number of qubits in the system  

We consider M/M/1/∞ systems with inventory in which completing each service in the queueing system requires an on-hand inventory. Continuous review (r, Q) policy is considered for the inventory system, and lead times are assumed to be mixed exponentially distributed. During stockout, arriving demands get rejected from the queue and become lost (lost sale situation). We derive stationary distribution of product form of joint queue length and on-hand inventory. The resulting distribution is employed to compute performance measures which can be used to derive the optimal policy. Optimal order size for predetermined reorder policy is initially determined and finally, optimal reorder point and... 

In this paper a two-echelon supply chain consisting of a supplier and aretailer is considered, Customers refer to retailer according to a Poissonprocess and retailer uses one for one inventory policy. Supplier followscontinuous review (r,Q) policy. Satisfying each demand which arrives to thesupplier needs an on hand-inventory and a process/service. Process/service andreplenishment lead times are random variables which are exponentiallydistributed. During a period that supplier has non zero on-hand inventory,arriving demands from retailer join the queue. But when supplier has no on-handinventory retailer buys product from the other source with zero lead time andadditional cost. In this paper... 

Visible light communication (VLC) uses LED lights for simultaneous illumination and data transmission. The throughput of a VLC network is highly dependent on the location of VLC access points (AP). In this paper, we propose a novel optimization framework for approximately optimal VLC AP placement which takes into account the stationary distribution of users for the first time. This distribution is the result of the mobility pattern of users in an indoor environment. The proposed method is independent of the resource allocation algorithm and eliminates the need for exhaustive simulations to find the optimal location for VLC APs. Simulation results show a significant improvement in the... 

In this paper, we propose an analytical approach to compute the probability of connectivity for one-dimensional ad hoc networks. The proposed analysis gives the exact probability of connectivity for an arbitrary distribution of nodes, provided that nodes are independently and identically distributed. We conduct separate analyses for two cases; in the first case, the number of nodes varies by time under a stationary distribution and in the second case, there is a fixed (known) number of nodes in the network. Using the approaches presented in this work, we are able to derive closed-form formulas for the probability of connectivity for some spatial distributions, while for more complicated... 

In this paper, we argue that in many basic algorithms for machine learning, including support vector machine (SVM) for classification, principal component analysis (PCA) for dimensionality reduction, and regression for dependency estimation, we need the inner products of the data samples, rather than the data samples themselves.Motivated by the above observation, we introduce the problem of private inner product retrieval for distributed machine learning, where we have a system including a database of some files, duplicated across some non-colluding servers. A user intends to retrieve a subset of specific size of the set of the inner product of every pair of data items in the database with...