G.C. Sharma

Maximum Entropy Approach for discrete-time unreliable server Geo X /Geo/1 queue with working vacation

This paper analyses a discrete-time GeoX/Geo/1 queue with unreliable server and working vacation. During the vacation period, the server renders service to the primary job at lower rate rather than completely stopping service; this type of vacation is considered as working vacation. For modelling the queueing problem, the inter-arrival time, service time and repair time are treated as discrete random variables. The customers are assumed to arrive at the system in batches according to a geometric process during the consecutive slots. Using the probability generating function method, we obtain the steady-state distribution of the number of the customers in the system. Furthermore, Maximum Entropy Approach (MEA) is employed to obtain the approximate formulae for the probability distributions of the number of customers and the expected waiting time in the system in terms of several well-known results. Finally, the sensitivity analysis is also carried out to illustrate the effect of different parameters on several performance characteristics.

A batch arrival retrial queuing system for essential and optional services with server breakdown and Bernoulli vacation

This paper studies a general retrial M X /G/1 queue with an additional phase of second optional service and Bernoulli vacation where breakdowns occur randomly at any instant while servicing the customers. If an arriving batch finds that the server is busy in providing either first essential service (FES)/second optional service (SOS) or on vacation then arriving batch enters an orbit called retrial queue. Otherwise, one customer from arriving batch starts to be served by the server while the rest join the orbit. The vacation times and service times of both first essential and second optional services are assumed to be general distributed while the retrial times are exponential distributed. Introducing supplementary variables and by employing embedded Markov chain technique, we derive some important performance measures of the system such as average orbit size, average queue size, mean waiting time, expected lengths of busy period, etc. Numerical results have been facilitated to illustrate the effect of different parameters on several performance measures.

M/M/R+r machining system with reneging, spares and interdependent controlled rates

The present investigation deals with the multi component machine repair problem by including the concepts of reneging and interdependent controlled rates. We consider a machining system consisting of M operating units, S 1 and S 2 warm spares of two kinds and a repair facility having R permanent repairmen and r additional removable repairmen. When all the spares are used and the operating units fail, the system works in degraded mode. By using interdependent controlled arrival and service rates and reneging parameters along with time-sharing concept, the queueing model is developed for more versatile situations encountered in production/ manufacturing industries. The solution is obtained by using recursive technique. The expressions for the queue size distribution and expected queue length are established. Some more performance indices such as expected number of failed units waiting for the service, expected number of busy repairmen, expected number of both types of spare parts functioning as standbys, etc., are obtained with the help of recursive technique. By taking numerical illustrations, the sensitivity analysis is provided to validate the analytical results.

Cost Analysis for a Supplier in an Inflationary Environment with Stock Dependent Demand Rate for Perishable Items

The present study is concerned with the cost modeling of an inventory system with perishable multi-items having stock dependent demand rates under an inflationary environment of the market. The concept of permissible delay is taken into account. The study provides the cost analysis of inventory system under the decision criteria of time value of money, inflation, deterioration, and stock dependent demand. Numerical illustrations are derived from the quantitative model to validate the results. The cost of inventory and optimal time are also computed by varying different system parameters. The comparison of these results is facilitated by computing the results with neurofuzzy results.

Call admission control and resource allocation of wireless networks

In the next-generation wireless communication, Orthogonal Frequency Division Multiplexing (OFDM) is a potential key technology. A CAC scheme is proposed for subcarrier allocation in OFDM-based wireless multi-service network. Call connection requests are divided into two classes: (i) narrowband calls and (ii) wideband calls. Traffic is characterised as batch arrival process for both classes of the calls, so that each call may request multiple subcarriers to satisfy its Quality of Service (QoS) requirement. There is a provision of buffer for narrowband calls, whereas the sub-rating scheme is used for wideband calls. The successive over-relaxation method is employed to solve the set of steady-state equations governing the traffic model. Various performance measures such as blocking probability of wide and narrowband calls, overall blocking probability of the calls and bandwidth utilisation are established. The sensitivity analysis has also been carried out to depict the effects of various system parameters on the performance measures.

Queueing analysis and channel assignment scheme for cellular radio system with GPRS services

In this investigation, we develop algorithm for cut-off priority for channel assignment in cellular radio network with buffering mechanism. The priority is given to GPRS handoff packets in comparison to new GPRS packets by reserving some channels for handoff services. Discouragement behaviours of the packets are also taken into account to deal with more realistic situations. The packets arrive in Poisson fashion whereas service time is exponentially distributed. Transient analysis based on matrix approach has been done to obtain the solution of the system of differential equations governing the traffic model. Various performance indices such as blocking probabilities of new packets, blocking probabilities of handoff packets and carried load, etc., are established in terms of transient probabilities. Furthermore, the analytical results are compared with adaptive network-based fuzzy inference system (ANFIS) approach. The sensitivity analysis has been performed to visualise the effects of various system parameters on the performance indices.

Performance prediction of machine repair problem with spares and two modes of failure

This investigation is concerned with the transient analysis of machine repair problem with M operating units and multi types of warm spares. In case when all spares are being used, the failure of units occurs in degraded fashion. Each unit is assumed to fail in two modes. When all permanent repairmen are busy, the caretaker who brings the failed units for repair departs from the system after waiting for sometime in the queue due to impatience. For transient state, Chapman–Kolmogorov equations governing the model are constructed. Various performance measures such as expected number of failed units in each mode, average number of operating units in the system, average number of idle and busy repairmen in the system, operative utilisation factor, etc., are obtained. The cost minimisation problem to determine the optimum number of spares in terms of various cost elements has been formulated. We used Runge–Kutta technique to find the numerical solution for the transient model. The sensitivity analysis is performed to observe the effect of different parameters on various performance indices.

State dependent M/M/1/WV queueing system with inspection, controlled arrival rates and delayed repair

The Markov model is developed to explore the performance analysis of a state dependent working vacation queueing system with interdependent rates. The server is subjected to breakdown randomly while providing services. When a breakdown occurs, the server is immediately sent to the repair station where the repairman takes a setup time before starting the repair. The failed server is inspected by the repairman and if there is minor problem, the server is repaired and is sent back to the service station with probability q. If some major fault is diagnosed during inspection, the server requires second phase of repair with probability p = 1 – q. The matrix geometric method is applied to obtain the queue size distribution and other performance indices such as throughput, expected delay time, etc. Various performance measures are computed for varying values of system parameters to facilitate the sensitivity analysis by taking a numerical illustration.

k-out of-n System with Dependent Failures and Standby Support

درسنا في ورقة البحث هذه نظاما وافرا جزئيا ( ك من بين ن ) يتعرض لحالات فشل يعتمد بعضها على بعض وبه وحدات احتياطية. إن فشل أية وحدة عاملة يؤثر في معولية النظام . كما أن دعم النظام بوحدات احتياطية يزيد من هذه المعولة ، واستهدافا لتحسين درجة جودة الخدمة قمنا بدراسة خيارين للدعم الاحتياطي للنظم المضمحلة، حيث قمنا باشتقاق تعبيرات للمعلومية ولزمن التشغيل المتوقع. وللتحقق من صحة النتائج التحليلية ، وفرنا أمثلة توضيحية تتضمن نتائج عددية .

Multi-component machine repair problem with unreliable repairman, reboot, imperfect recovery and retrial

The present study aims at the performance prediction of a multi-component machining system comprised of operating and mixed warm standby units under the care of a single unreliable server and retrial attempts. The concepts of reboot and recovery are incorporated to portray the real time manufacturing/production system dealing with automatic machines. A failed unit is automatically detected and fixed with a coverage probability. In case of unsuccessful recovery, the fault is cleared by reboot or reset operation. If the server is in idle state, the person taking care of the failed units joins the orbit and retries again and again for the repair of the failed units. To explore the transient state behaviour of the machine repair system, we establish various performance measures in terms of transient state probabilities of the number of failed units present in the system. Further, a comparative analysis of performance measures is presented for different system configuration. The feasibility of implementation of soft-computing technique is explored by computing the performance measures using adaptive network-based fuzzy interference systems (ANFIS).