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This paper aims to consider a single server queue with system disasters and impatience behavior are evident in our daily life. For this purpose, authors require to know the general behavior of these systems. Transient analysis shows for us how the system will operate up to some time instant t.

In this paper, authors consider a single server queue with system disaster and impatient behavior of customers in a multi-phase random environment, in which the system transits to a repair state after each system disaster. When the system is in a failure phase or going through a repair phase, the new arrivals would be impatient. In case the system is not repaired before the customer’s time expires, the customer would leave the queue and never return. Moreover, after repair, the system becomes ready for service in an operative phase with probability $q_{i} \ge 0.$. Using generating functions along with continued fractions and some properties of the confluent hypergeometric function, authors obtained on their own results.

Explicit expressions have been obtained for the time-dependent probabilities of the underlying queuing model. Also, time-dependent mean and variance of customers in the system are deduced.

The system authors are dealing with is somewhat complicated, there are some performance measures that cannot be achieved, but some of them have been obtained, such as the expectation and variance of the number of customers in the system.

Based on the obtained results, some numerical examples are some numerical examples are presented to illustrate the effect of various parameters on the behavior of the proposed system.

Authors’ studied transient analysis of a single server queue with system disaster and impatient customer system is suitable for behavior interpretation of many systems in our lives, such as telecommunication networks, inventory systems and impatient telephone switchboard customers, manufacturing system and service system.

To the best of the author’s/authors’ knowledge and according to the literature survey, in a multi-phase random environment, no previous published article is presented for transient analysis of a single server queue with system disaster and impatient customer behavior in a random environment.

The purpose of this paper is to provide a traffic route selection strategy based on minimum carbon dioxide (CO₂) emission by vehicles over different route choices.

The study used queuing theory for Markovian M/M/1 model over the road junctions to assess total time spent over each of the junctions for a route with junctions in tandem. With parameters of distance, mean service rate at the junction, the number of junctions and fuel consumption rate, which is a function of variable average speed, the CO₂ emission is estimated over each of the junction in tandem and collectively over each of the routes.

The outcome of the study is a mathematical formulation, using queuing theory to estimate CO₂ emissions over different route choices. Research finding estimated total time spent and subsequent CO₂ emission for mean arrival rates of vehicles at junctions in tandem. The model is validated with a pilot study, and the result shows the best vehicular route choice with minimum CO₂ emissions.

Proposed study is limited to M/M/1 model at each of the junction, with no defection of vehicles. The study is also limited to a constant mean arrival rate at each of the junction.

The work can be used to define strategies to route vehicles on different route choices to reduce minimum vehicular CO₂ emissions.

Proposed work gives a solution for minimising carbon emission over routes with unsignalised junctions in the tandem network.

This study is carried out in one public and one private health-care centers based on different probabilities of patient’s no-show rate. The present study aims to determine the optimal queuing system capacity so that the expected total cost is minimized.

In this study an M/M/1/K queuing model is used for analytical properties of optimal queuing system capacity and appointment window so that total costs of these cases could be minimized. MATLAB software version R2014a is used to code the model.

In this paper, the optimal queuing system capacity is determined based on the changes in effective parameters, followed by a sensitivity analysis. Total cost in public center includes the costs of patient waiting time and rejection. However, the total cost in private center includes costs of physician idle time plus costs of public center. At the end, the results for public and private centers are compared to reach a final assessment.

Today, determining the optimal queuing system capacity is one of the most central concerns of outpatient clinics. The large capacity of the queuing system leads to an increase in the patient’s waiting-time cost, and on the other hand, a small queuing system will increase the cost of patient’s rejection. The approach suggested in this paper attempts to deal with this mentioned concern.

Computer networks are very complex and somewhat unpredictable systems in dynamic operations. Cybernetic modelling, incorporating stochastic, fuzzy variables, wherever appropriate, approximating interactions not easily tractable via a black‐box systems approach, may be more accurate. A method of analysis of computer networks is considered by representing subsystems and interactions, accurately as far as possible, and then utilising the results of systems sciences for analysis, including specifics, e.g. queuing systems. The aim is to identify correspondences between the behaviour of subsystems of networks and suitable analytic tools. Automation along such lines for the analysis and design of networks and other systems may be a possibility.

As new computer communication systems, such as distributed computer networks or mobile data networks, grow in scale and complexity, the problem of being able to understand and to predict system behaviour becomes increasingly important. To their behaviour analysis we can use both analytical and simulation methods. Principally the application of analytical queuing theory results belongs to the preferred method in comparison to the simulation method. In this sense the article describes the development, realisation and verification of the new analytical model for the study of the basic parameters (end‐to‐end delay, performance etc.) of distributed data networks (computer networks, mobile data networks). The suggested model considers for every node of the data network one part for its own node's activities (communication functions) and another one for the modelling of each node channel for data transmission. When using a multiprocessor system, as the modern node communication processor, the model for its own node activities is the more realistic M/D/r system (Poisson arrival process/Deterministic service time distribution/r server system) and for the every node transmission channel the M/M/1 system (Exponential service time, Single server system). The new developed analytical model includes the influence of the communication functions to the whole delay in each node of a computer communication network. The achieved results of the developed model are compared with the results of the commonly used analytical and simulation models to estimate the magnitude of improvement. Likewise the developed analytical model was tested under various ranges of parameters, which influence the architecture of the distributed data networks and which are important for practical use.

The purpose of this paper is to investigate into the improvement strategies for lead time reduction of military aircraft major overhaul (enhance the overhaul task from present seven to nine-plus aircrafts as agreed to customer) for ABC Company.

This research has been conducted based on the available knowledge and extensive experience gained while working in the overhaul unit of the case organization for a long period of time. The research employs an integrated approach of multi-criteria decision method (in specific analytic hierarchy process (AHP)), theory of constraint (TOC) and simulation for M/M/1/K queuing environment for investigating the improvement strategies for lead time reduction in major overhaul of military aircraft. This has mainly included: Step 1: analysis of existing activity network using actual overhaul data; Step 2: ranking of constraint activities that most affects the lead time using AHP; Step 3: revised flow activity network using time buffers (TBs) concept of TOC; Step 4: mathematical model formulation for effective utilization of TB using single server finite queuing approach (M/M/1/K queuing environment); Step 5: discrete event simulation representing present overhaul conditions and revised overhaul conditions with different scenarios; and Step 6: sensitivity analysis and interpretation of results. The proposed methodology has been tested on an industrial case study dealing with an aircraft overhaul in India (namely ABC Company).

The proposed overhaul lead-time reduction plan points out the augmentation of resources in order to achieve more than 50 per cent reduction in lead time and waiting time under two scenarios – with overtime and without overtime.

An integrated approach proposed has so far been applicable to the specific aircrafts (Jaguar/Mirage/Kiran) of the ABC Company overhaul division. However, the particular methodology can be proved potentially useful and highly practical when applying to other aircraft types.

The results indicate several problems with the current overhaul strategies that need focused process improvements and a need for capacity augmentation for achieving the enhanced overhaul task of nine+ aircrafts per year with reduced overhaul lead time. The proposed approach also provides the maintenance planners with a platform for decision analysis and support often ignored the capacity augmentation.

This paper aims to study the corresponding optimal service strategies and pricing in the styled non-preemptive M/M/1 service systems from different objectives, which consider both heterogeneous waiting costs of customers and service values in customer segmentation.

In this paper, the authors consider two service situations where customers cannot leave the service system (i.e. monopoly service system) and customers can leave the service system freely (i.e. non-monopoly service system), respectively. The authors study the following four different perspectives that are revenue, social welfare, social cost and utility of customers. The authors first build up a new model, then propose the related objective functions. Further, the authors optimize the corresponding functions and achieve the optimal results. Later, the authors propose the corresponding optimal strategies. Finally, the authors use a practical numerical case to verify the proposed results.

The results of this paper indicates that the service provider should adopt classification services to gain the maximum revenue, the maximum social welfare and the minimum social costs by charging a priority fee in above two service systems. However, the service provider should cancel customer classification and keep regular customer only to obtain maximum utility. In the monopoly service system, both the optimal proportion priority customers and the revenue decrease with the increasing of the service rate, while in a non-monopoly service system, both of them are increasing with the service rate improving.

This paper first considers both heterogeneity of service values and waiting costs in queuing system, then the author set up a new model based on this assumption. Moreover, the authors draw the corresponding management insights based on the optimal results, which were unavailable before.

This paper considers correction aspects of computer communication networks modelling with emphasis on their performance evaluation. In general, the problem is to achieve the highest possible performance given constraints on the system.

The paper reviews the application of the analytical methods, based on the queueing theory, to the computer communication systems and makes an extension of theory to the improvement of the developed analytical models. In this sense the paper describes the derivation of a correction factor for analytical models to study more precise their basic parameters (end‐to‐end delay, performance, etc.).

The contribution is in incorporating the derived correction factor to account for the real non‐exponential nature of the input to the transmission channels of computer communication systems. The produced results by corrected analytical model are compared with results previously reported in the literature to estimate the magnitude of improvement.

The improved analytical models were tested under various ranges of parameters, which influence the architecture of the computer communication networks and which are important for practical use.

The rapid rate of growth of computer‐based communication systems (e.g. distributed computer networks, mobile data networks) has resulted in a renewed and intensive interest in this area. Efficient design of their service facilities leads to the sharing of resources among users. Such public shared networks are largely oversubscribed by independent users, which make random demands on the network resources. The optimal resource allocation to satisfy such demands and the proper settlement of contention when demands exceed the capacity of the resources, constitute the problem of being able to understand and to predict system behaviour.

To behaviour analysis we can use both analytical and simulation methods. Modelling and simulation are methods, which are commonly used by performance analysts to represent constraints and optimise performance. Principally the application of analytical queuing theory results belongs to the preferred method in comparison to the simulation method, because of their ability to analyse also very large networks.