Adjoining Batch Markov Arrival Processes of a Markov Chain

A batch Markov arrival process（BMAP） X^＊=（N, J） is a 2-dimensional Markov process with two components, one is the counting process N and the other one is the phase process J. It is proved that the phase process is a time-homogeneous Markov chain with a finite state-space, or for short, Markov chain. In this paper,a new and inverse problem is proposed firstly： given a Markov chain J, can we deploy a process N such that the 2-dimensional process X^＊=（N, J） is a BMAP？ The process X^＊=（N, J） is said to be an adjoining BMAP for the Markov chain J. For a given Markov chain the adjoining processes exist and they are not unique. Two kinds of adjoining BMAPs have been constructed. One is the BMAPs with fixed constant batches, the other one is the BMAPs with independent and identically distributed（i.i.d） random batches. The method we used in this paper is not the usual matrix-analytic method of studying BMAP, it is a path-analytic method. We constructed directly sample paths of adjoining BMAPs. The expressions of characteristic（D_k, k = 0, 1, 2· · ·）and transition probabilities of the adjoining BMAP are obtained by the density matrix Q of the given Markov chain J. Moreover, we obtained two frontal Theorems. We present these expressions in the first time.

CONSTRUCTION OF CONTINUOUS TIME MARKOVIAN ARRIVAL PROCESSES

Markovian arrival processes were introduced by Neuts in 1979 （Neuts 1979） and have been used extensively in the stochastic modeling of queueing, inventory, reliability, risk, and telecommunications systems. In this paper, we introduce a constructive approach to define continuous time Markovian arrival processes. The construction is based on Poisson processes, and is simple and intuitive. Such a construction makes it easy to interpret the parameters of Markovian arrival processes. The construction also makes it possible to establish rigorously basic equations, such as Kolmogorov differential equations, for Markovian arrival processes, using only elementary properties of exponential distributions and Poisson processes. In addition, the approach can be used to construct continuous time Markov chains with a finite number of states

SINGLE SERVER QUEUES WITH A BATCH MARKOVIAN ARRIVAL PROCESS AND BULK RENEWAL OR NON-RENEWAL SERVICE

We first consider an infinite-buffer single server queue where arrivals occur according to a batch Markovian arrival process （BMAP）. The server serves customers in batches of maximum size ＇b＇ with a minimum threshold size ＇a＇. The service time of each batch follows general distribution independent of each other as well as the arrival process. The proposed analysis is based on the use of matrix-analytic procedure to obtain queue-length distribution at a post-departure epoch. Next we obtain queue-length distributions at various other epochs such as, pre-arrival, arbitrary and pre-service using relations with post-departure epoch. Later we also obtain the system-length distributions at post-departure and arbitrary epochs using queue-length distribution at post-departure epoch. Some important performance measures, like mean queue-lengths and mean waiting times have been obtained Total expected cost function per trait time is also derived to determine the locally optimal values of a and b. Secondly, we perform similar analysis for the corresponding infinite-buffer single server queue where arrivals occur according to a BMAP and service process in this case follows a non-renewal one, namely, Markovian service process （MSP）.

ANALYSIS OF A PRODUCTION-INVENTORY MODEL WITH ERLANGIAN DEMAND ARRIVAL PROCESS

We study a production-inventory system having a machine, a storage facility. The demand for the product is governed by an Erlangian demand arrival process, where demand sizes are independent and identically distributed random variables. A two-criticalnumber policy (m, M) is used to control a machine's setups and shutdowns, namely, a machine is shut down whenever the inventory level reaches M, and resumes operating only when the inventory level falls below the critical number m(m ≤ M). We obtain the steady state distribution of the inventory process and some performance measures of the process.

On a risk model with Markovian arrivals and tax

A risk model with Markovian arrivals and tax payments is considered.When the insurer is in a profitable situation,the insurer may pay a certain proportion of the premium income as tax payments.First,the Laplace transform of the time to cross a certain level before ruin is discussed.Second,explicit formulas for a generalized Gerber-Shiu function are established in terms of the＇original＇Gerber-Shiu function without tax and the Laplace transform of the first passage time before ruin.Finally,the differential equations satisfied by the expected accumulated discounted tax payments until ruin are derived.An explicit expression for the discounted tax payments is also given.

The MAP/PH(PH/PH)/1 Discrete-time Queuing System with Repairable Server

In this paper, we discuss a discrete time repairable queuing system with Markovian arrival process, where lifetime of server, service time and repair time of server are all discrete phase type random variables. Using the theory of matrix geometric solution, we give the steady state distribution of queue length and waiting time. In addition, the stable availability of the system is also provided.

Performance Evaluation of Mobility Anchor Point with Guard Load Reservation in Hierarchical Mobile IPv6

Hierarchical mobile IPv6 （HMIPv6） introduces a mobility anchor point to reduce the signaling overhead and handoff latency. In this paper, we apply the matrix-analytical approach to explore the performance measures of the ongoing mobile nodes （MNs） drop and new MNs block probabilities of mobility anchor point with a guard bandwidth reservation scheme. We apply the Markovian arrival process （MAP） to model ongoing MNs and new MNs. Five related performance measures are derived, including the long-term new MN block and ongoing MN drop probabilities, and the three short-term measures of average length of a block period and a non-block period, as well as the conditional ongoing MN drop probability during a block period. These performance measures greatly assist the guard bandwidth reservation mechanism in determining a proper threshold guard bandwidth. The results presented in this paper can provide guidelines for designing adaptive algorithms to adjust the threshold in the guard bandwidth reservation scheme.

Total duration of negative surplus for a MAP risk model

In this paper, we study the risk model with Markovian arrivals where we allow the surplus process to continue if the surplus falls below zero. We first derive expressions for the severity of ruin. Then by using the strong Markovian property of a two-dimensional Markov process and the expression for the severity of ruin, we obtain the Laplace transform of the total duration of negative surplus.

Computational analysis of(MAP_1,MAP_2)/(PH_1,PH_2)/N queues with finite buffer in wireless cellular networks

This paper studies a queueing model with the finite buffer of capacity K in wireless cellular networks, which has two types of arriving calls--handoff and originating calls, both of which follow the Markov arriving process with different rates. The channel holding times of the two types of calls follow different phase-type distributions. Firstly, the joint distribution of two queue lengths is derived, and then the dropping and blocking probabilities, the mean queue length and the mean waiting time from the joint distribution are gotten. Finally, numerical examples show the impact of different call arrival rates on the performance measures.

DOA estimation via sparse recovering from the smoothed covariance vector

A direction of arrival（DOA） estimation algorithm is proposed using the concept of sparse representation. In particular, a new sparse signal representation model called the smoothed covariance vector（SCV） is established, which is constructed using the lower left diagonals of the covariance matrix. DOA estimation is then achieved from the SCV by sparse recovering, where two distinguished error limit estimation methods of the constrained optimization are proposed to make the algorithms more robust. The algorithm shows robust performance on DOA estimation in a uniform array, especially for coherent signals. Furthermore, it significantly reduces the computational load compared with those algorithms based on multiple measurement vectors（MMVs）. Simulation results validate the effectiveness and efficiency of the proposed algorithm.

The MAP/PH/N Retrial Queue in a Random Environment

We consider the MAP/PH/N retrial queue with a finite number of sources operating in a finite state Markovian random environment. Two different types of multi-dimensional Markov chains are investigated describing the behavior of the system based on state space arrangements. The special features of the two formulations are discussed. The algorithms for calculating the stationary state probabilities are elaborated, based on which the main performance measures are obtained, and numerical examples are presented as well.

On a BMAP/G/1 G-queue with Setup Times and Multiple Vacations

In this paper, we consider a BMAP/G/1 G-queue with setup times and multiple vacations. Arrivals of positive customers and negative customers follow a batch Markovian arrival process （BMAP） and Markovian arrival process （MAP） respectively. The arrival of a negative customer removes all the customers in the system when the server is working. The server leaves for a vacation as soon as the system empties and is allowed to take repeated （multiple） vacations. By using the supplementary variables method and the censoring technique, we obtain the queue length distributions. We also obtain the mean of the busy period based on the renewal theory.

Performance of the(BMAP_1, BMAP_2 )/(PH_1, PH_2 )/N Retrial Queueing System with Finite Buffer

This paper consider the （BMAP1, BMAP2）/（PH1, PH2）/N retrial queue with finite-position buffer. The behavior of the system is described in terms of continuous time multi-dimensional Markov chain. Arriving type I calls find all servers busy and join the buffer, if the positions of the buffer are insufficient, they can go to orbit. Arriving type II calls find all servers busy and join the orbit directly. Each server can provide two types heterogeneous services with Phase-type （PH） time distribution to every arriving call （including types I and II calls）, arriving calls have an option to choose either type of services. The model is quite general enough to cover most of the systems in communication networks. We derive the ergodicity condition, the stationary distribution and the main performance characteristics of the system. The effects of various parameters on the system performance measures are illustrated numerically.

A Stochastic Inventory System with Postponed Demands and Infinite Pool in Discrete-Time Setup

In this article,we consider a discrete-time inventory model in which demands arrive according to a discrete Markovian arrival process.The inventory is replenished according to an es;ST policy,and the lead time is assumed to follow a discrete phase-type distribution.The demands that occur during stock-out periods either enter a pool which has an infinite capacity or leave the system with a predefined probability.The demands in the pool are selected one by one,if the on-hand inventory level is above s t 1;and the interval time between any two successive selections is assumed to have a discrete phase-type distribution.The joint probability distribution of the number of customers in the pool and the inventory level is obtained in the steady-state case.We derive the system performance measures under steady state and using these measures,the total expected cost rate of the system is calculated.The impacts of arrival rate on the performance measures are graphically illustrated.Finally,we study the impact of cost on the optimal values of the total expected cost rate,inventory level and the reorder point.

Source localization using a non-cocentered orthogonal loop and dipole (NCOLD) array

A uniform array of scalar-sensors with intersensor spacings over a large aperture size generally offers enhanced resolution and source localization accuracy,but it may also lead to cyclic ambiguity.By exploiting the polarization information of impinging waves,an electromagnetic vector-sensor array outperforms the unpolarized scalar-sensor array in resolving this cyclic ambiguity.However,the electromagnetic vector-sensor array usually consists of cocentered orthogonal loops and dipoles（COLD）,which is easily subjected to mutual coupling across these cocentered dipoles/loops.As a result,the source localization performance of the COLD array may substantially degrade rather than being improved.This paper proposes a new source localization method with a non-cocentered orthogonal loop and dipole（NCOLD）array.The NCOLD array contains only one dipole or loop on each array grid,and the intersensor spacings are larger than a half-wavelength.Therefore,unlike the COLD array,these well separated dipoles/loops minimize the mutual coupling effects and extend the spatial aperture as well.With the NCOLD array,the proposed method can effciently exploit the polarization information to offer high localization precision.

An M^([X])/G/1 Retrial G-queue with Single Vacation Subject to the Server Breakdown and Repair

An M[X]/G/1 retrial G-queue with single vacation and unreliable server is investigated in this paper. Arrivals of positive customers form a compound Poisson process, and positive customers receive service immediately if the server is free upon their arrivals; Otherwise, they may enter a retrial orbit and try their luck after a random time interval. The arrivals of negative customers form a Poisson process. Negative customers not only remove the customer being in service, but also make the server under repair. The server leaves for a single vacation as soon as the system empties. In this paper, we analyze the ergodical condition of this model. By applying the supplementary variables method, we obtain the steady-state solutions for both queueing measures and reliability quantities.