Retrial Queues with Orbital Search

Queueing system in which arriving customers who find all servers and waiting positions (if any) occupied many retry for service after a period of time are retrial queues or queues with repeated attempts. This study deals with two objectives one is to introduce orbital search in retrial queueing models which allows to minimize the idle time of the server. If the holding costs and cost of using the search of customers will be introduced, the results we obtained can be used for the optimal tuning of the parameters of the search mechanism. The second one is to provide insight of the link between the corresponding retrial queue and the classical queue. At the end we observe that when the search probability Pj = 1 for all j, the model reduces to the classical queue and when Pj = 0 for all j, the model becomes the retrial queue. It discusses the performance evaluation of single-server retrial queue. It was determined by using Poisson process. Then it discuss the structure of the busy period and its analysis interms of Laplace transforms and also provides a direct method of evaluation for the first and second moments of the busy period. Then it discusses the M/ PH/1 retrial queue with disaster to the unit in service and orbital search, and a multi-server retrial queueing model (MAP/M/c) with search of customers from the orbit. MAP is convenient tool to model both renewal and non-renewal arrivals. Finally the present model deals with back and forth movement between classical queue and retrial queue. In this model when orbit size increases, retrial rate also correspondingly increases thereby reducing the idle time of the server between services

Analysis of Some Stochastic Inventory Models with Pooling Retrial of Customers

The thesis deals with analysis of some Stochastic Inventory Models with Pooling/Retrial of Customers.. In the first model we analyze an (s,S) production Inventory system with retrial of customers. Arrival of customers from outside the system form a Poisson process. The inter production times are exponentially distributed with parameter µ. When inventory level reaches zero further arriving demands are sent to the orbit which has capacity M(<∞). Customers, who find the orbit full and inventory level at zero are lost to the system. Demands arising from the orbital customers are exponentially distributed with parameter γ. In the model-II we extend these results to perishable inventory system assuming that the life-time of each item follows exponential with parameter θ. The study deals with an (s,S) production inventory with service times and retrial of unsatisfied customers. Primary demands occur according to a Markovian Arrival Process(MAP). Consider an (s,S)-retrial inventory with service time in which primary demands occur according to a Batch Markovian Arrival Process (BMAP). The inventory is controlled by the (s,S) policy and (s,S) inventory system with service time. Primary demands occur according to Poissson process with parameter λ. The study concentrates two models. In the first model we analyze an (s,S) Inventory system with postponed demands where arrivals of demands form a Poisson process. In the second model, we extend our results to perishable inventory system assuming that the life-time of each item follows exponential distribution with parameter θ. Also it is assumed that when inventory level is zero the arriving demands choose to enter the pool with probability β and with complementary probability (1- β) it is lost for ever. Finally it analyze an (s,S) production inventory system with switching time. A lot of work is reported under the assumption that the switching time is negligible but this is not the case for several real life situation.

Photophysical and Electrochemical Investigations on Photoconducting Poly(6-tert-butyl-3,4-dihydro-2H- 1,3-benzoxazine)

Poly(6-tert-butyl-3,4-dihydro-2H-1,3-benzoxazine) was synthesized by thermally activated cationic ring opening polymerization. The structure of the polymer was confirmed by spectral and thermal studies. The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) were estimated using cyclic voltammetry and optical absorption. Modulated photocurrent measurement technique was employed to study the spectral and field dependence of photocurrent. Photocurrent of the order of 1.5 micro A/m2 was obtained for polymer at a biasing electric field of 40 V/mico m.

OPTIMAL UTILIZATION OF SERVICE FACILITY FOR A k-OUT-OF-n SYSTEM WITH REPAIR BY EXTENDING SERVICE TO EXTERNAL CUSTOMERS IN A RETRIAL QUEUE

In this paper, we study a k-out-of-n system with single server who provides service to external customers also. The system consists of two parts:(i) a main queue consisting of customers (failed components of the k-out-of-n system) and (ii) a pool (of finite capacity M) of external customers together with an orbit for external customers who find the pool full. An external customer who finds the pool full on arrival, joins the orbit with probability and with probability 1− leaves the system forever. An orbital customer, who finds the pool full, at an epoch of repeated attempt, returns to orbit with probability (< 1) and with probability 1 − leaves the system forever. We compute the steady state system size probability. Several performance measures are computed, numerical illustrations are provided.

ON (s,S) inventory policy with/without retrial and interruption of services/production

In this thesis we have developed a few inventory models in which items are served to the customers after a processing time. This leads to a queue of demand even when items are available. In chapter two we have discussed a problem involving search of orbital customers for providing inventory. Retrial of orbital customers was also considered in that chapter; in chapter 5 also we discussed retrial inventory model which is sans orbital search of customers. In the remaining chapters (3, 4 and 6) we did not consider retrial of customers, rather we assumed the waiting room capacity of the system to be arbitrarily large. Though the models in chapters 3 and 4 differ only in that in the former we consider positive lead time for replenishment of inventory and in the latter the same is assumed to be negligible, we arrived at sharper results in chapter 4. In chapter 6 we considered a production inventory model with production time distribution for a single item and that of service time of a customer following distinct Erlang distributions. We also introduced protection of production and service stages and investigated the optimal values of the number of stages to be protected.

Synthesis, characterization and physiochemical information, along with antimicrobial studies of some metal complexes derived from an ON donor semicarbazone ligand

Eight new transition metal complexes of benzaldehyde-N(4)–phenylsemicarbazone have been synthesized and characterized by elemental analyses, molar conductance, electronic and infrared spectral studies. In all the complexes, the semicarbazone is coordinated as neutral bidentate ligand. 1H NMR spectrum of [Zn(HL)2(OAc)2] shows that there is no enolisation of the ligand in the complex. The magnetic susceptibility measurements indicate that Cr(III), Mn(II), Fe(III), Co(II) and Cu(II) complexes are paramagnetic and Ni(II) is diamagnetic. The EPR spectrum of [Mn(HL)2(OAc)2] in DMF solution at 77K shows hyperfine sextet with low intensity forbidden lines lying between each of the two main hyperfine lines. The g values calculated for the [Cu(HL)2SO4] complex in frozen DMF, indicate the presence of unpaired electron in the dx2−y2 orbital. The metal ligand bonding parameters evaluated showed strong in-plane bonding and in-plane bonding. The ligand and complexes were screened for their possible antimicrobial activities.

Synthesis, spectral characterization and crystal structure of copper(II) complexes of 2-benzoylpyridine-N(4)-phenylsemicarbazone

An interesting series of nine new copper(II) complexes [Cu2L2(OAc)2] H2O (1), [CuLNCS] ½H2O (2), [CuLNO3] ½H2O (3), [Cu(HL)Cl2] H2O (4), [Cu2(HL)2(SO4)2] 4H2O (5), [CuLClO4] ½H2O (6), [CuLBr] 2H2O (7), [CuL2] H2O (8) and [CuLN3] CH3OH (9) of 2-benzoylpyridine-N(4)-phenyl semicarbazone (HL) have been synthesized and physico-chemically characterized. The tridentate character of the semicarbazone is inferred from IR spectra. Based on the EPR studies, spin Hamiltonian and bonding parameters have been calculated. The g values, calculated for all the complexes in frozen DMF, indicate the presence of the unpaired electron in the dx2 y2 orbital. The structure of the compound, [Cu2L2(OAc)2] (1a) has been resolved using single crystal X-ray diffraction studies. The crystal structure revealed monoclinic space group P21/n. The coordination geometry about the copper(II) in 1a is distorted square pyramidal with one pyridine nitrogen atom, the imino nitrogen, enolate oxygen and acetate oxygen in the basal plane, an acetate oxygen form adjacent moiety occupies the apical position, serving as a bridge to form a centrosymmetric dimeric structure