We consider a firm which targets a certain level of customer responsiveness with a minimum operat... more We consider a firm which targets a certain level of customer responsiveness with a minimum operational cost. The firm employs a preorder strategy, in which customers place their orders before their actual need based on a predefined time window called commitment lead time and, in turn, they receive a bonus. The firm aims to determine the optimal control policy, which consists of the optimal commitment lead time and the optimal base-stock level, such that the total operational cost is minimized subject to a time-based service level target. We formulate two time-based service criteria to measure the firm's responsiveness in terms of average customer waiting time and individual customer waiting time in two constraint optimization models called ACO and CCO, respectively. We derive the exact probability distribution of customer waiting time, and we propose exact and heuristic optimization algorithms to solve the ACO and CCO models. We show that the commitment lead time not only increases the firm's responsiveness level but also decreases the customers' maximum waiting time. We find that when the firm targets a high level of responsiveness, the value of commitment lead time is more highlighted. We study multiple interesting extensions with two customer classes, random replenishment lead times and a combined model with two time-based service level targets.
European Journal of Operational Research, Apr 1, 2021
Many intra-logistics systems, such as automated container terminals, distribution warehouses, and... more Many intra-logistics systems, such as automated container terminals, distribution warehouses, and crossdocks, observe parallel process flows, which involve simultaneous (parallel) operations of independent resources while processing a job. When independent resources work simultaneously to process a common job, the effective service requirement of the job is difficult to estimate. For modeling simplicity, researchers tend to assume sequential operations of the resources. In this paper, we propose an efficient modeling approach for parallel process flows using two-phase servers. We develop a closed queuing network model to estimate system performance measures. Existing solution methods can evaluate the performance of closed queuing networks that consist of two-phase servers with exponential service times only. To solve closed queuing networks with general two-phase servers, we propose new solution methods: an approximate mean value analysis and a network aggregation dis-aggregation approach. We derive insights on the accuracy of the solution methods from numerical experiments. Although both solution methods are quite accurate in estimating performance measures, the network aggregation disaggregation approach consistently performs best. We illustrate the proposed modeling approach for two intra-logistic systems: a container terminal with automated guided vehicles and a shuttle-based compact storage system. Results show that approximating the simultaneous operations as sequential operations underestimates the container terminal throughput on average by 28% and at maximum up to 47%. Similarly, considering sequential operations of the resources in the compact storage system results in an underestimation of the throughput capacity up to 9%.
We study a multi-location inventory problem with a so-called quick response warehouse. In case of... more We study a multi-location inventory problem with a so-called quick response warehouse. In case of a stock-out at a local warehouse, the demand might be satisfied by a stock transfer from the quick response warehouse. We derive the optimal policy for when to accept and when to reject such a demand at the quick response warehouse. We also derive conditions under which it is always optimal to accept these demands. Furthermore, we conduct a numerical study and consider model variations.
The Medium Access Control (MAC) scheme proposed by DAVIC/DVB, IEEE 802.14 and DOCSIS for the upst... more The Medium Access Control (MAC) scheme proposed by DAVIC/DVB, IEEE 802.14 and DOCSIS for the upstream channel of Hybrid Fiber Coaxial (HFC) access networks is based on a mixable contention-based/contention-less time slot assignment. Contention-less slots are assigned by the head end to end stations according to a reservation scheme. Contentionbased slots are randomly accessed by active terminals without any preliminary allocation, so that collisions may occur. To resolve contention, the contention tree algorithm has been widely accepted by the DVB/DAVIC, IEEE 802.14 and DOCSIS standards for MAC because of higher throughput and lower access delay. In this paper we propose a novel contention resolution mechanism and compare its performance with that of existing procedures. The proposed procedure is termed as static arrival slot mechanism. In this mechanism, one slot in each frame is exclusively reserved for new arrivals that wish to access the channel using contention resolution, and at least one slot is reserved for resolving their contention if there was one in the arrival slot. The performance of the proposed mechanism is evaluated through analysis and simulation. The results show that the proposed mechanism outperforms existing contention resolution procedures under heavy traffic.
In this paper, we present and analyze a mathematical model for the computation of the system avai... more In this paper, we present and analyze a mathematical model for the computation of the system availability for a system of parallel machines with redundancies and repair priorities. Using the presented models, we show that the repair priorities have a strong effect on the performance of the system.
Proceedings Title: Proceedings of the 2012 Winter Simulation Conference (WSC), 2012
Magnetic Resonance Imaging (MRI) requires expensive diagnostic equipment and is labor intensive. ... more Magnetic Resonance Imaging (MRI) requires expensive diagnostic equipment and is labor intensive. To evaluate the effective use of the MRI resources a curve of flow time versus throughput may be helpful in quantifying the trade-off between patient waiting time and resource utilization, and in providing insight into operational time losses and variability. This curve may be obtained by simulation. However, building a detailed simulation model of an MRI department requires expertise typically unavailable in hospitals. To overcome this difficulty, we seek for an appropriate aggregate model of the MRI department, either a simulation or an analytical model. The aggregate model parameters are to be determined from hospital patient arrival and departure times. We study three different aggregate models for use in the MRI setting. To be able to evaluate the prediction accuracy of the candidate aggregate models we use a detailed simulation model as virtual MRI department.
Cardiothoracic surgery planning involves different resources such as operating theatre time, beds... more Cardiothoracic surgery planning involves different resources such as operating theatre time, beds, IC beds and nursing staff. In practice the planning in the Thorax Centre focuses on optimal use of operating theatre time, though the performance of the Thorax Centre as a whole is often more limited by the capacity of the IC. For operating theatres a master surgical schedule is used to allocate operating theatre resources at tactical level for a longer period. Operational schedules at weekly level are derived from this master schedule. Within cardiothoracic surgery different categories of patients can be distinguished on behalf of their requirement of resources. The mix of patients is, therefore, an important decision variable for the Thorax Centre to manage the use of these resources. In the paper we will consider the planning problem to generate a master operation schedule that realises a given target of patient throughput and optimises an object function for the utilisation of resources. This problem can be mathematically approached by mixed integer programming. We will discuss the mathematical model developed for this planning problem, the implementation in a decision support model for tactical surgery planning, the results obtained and the way the model can help to broaden the focus of planning of cardiothoracic patients.
DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428), 2003
The Medium Access Control (MAC) scheme proposed by DAVIC/DVB, IEEE 802.14 and DOCSIS for the upst... more The Medium Access Control (MAC) scheme proposed by DAVIC/DVB, IEEE 802.14 and DOCSIS for the upstream channel of Hybrid Fiber Coaxial (HFC) access networks is based on a mixable contention-based/contention-less time slot assignment. Contention-less slots are assigned by the head end to end stations according to a reservation scheme. Contentionbased slots are randomly accessed by active terminals without any preliminary allocation, so that collisions may occur. To resolve contention, the contention tree algorithm has been widely accepted by the DVB/DAVIC, IEEE 802.14 and DOCSIS standards for MAC because of higher throughput and lower access delay. In this paper we propose a novel contention resolution mechanism and compare its performance with that of existing procedures. The proposed procedure is termed as static arrival slot mechanism. In this mechanism, one slot in each frame is exclusively reserved for new arrivals that wish to access the channel using contention resolution, and at least one slot is reserved for resolving their contention if there was one in the arrival slot. The performance of the proposed mechanism is evaluated through analysis and simulation. The results show that the proposed mechanism outperforms existing contention resolution procedures under heavy traffic.
This paper develops an analytical model of sequential zone picking systems. The systems belong to... more This paper develops an analytical model of sequential zone picking systems. The systems belong to the most popular internal transport and order picking systems in practice, due to their scalability, flexibility, highthroughput ability, and fit-for-use for a wide range of products and order profiles. The major disadvantage of such systems, though, is congestion and blocking under heavy use, leading to long order lead times. In order to diminish blocking and congestion most systems make use of a dynamic block-and-recirculate protocol. The various elements of the system, like conveyor lanes and the pick zones, are modeled as a network of queues with multiple order classes and with capacity constraints on subnetworks, including the dynamic block-and-recirculate protocol. Due to this protocol, however, the stationary distribution of the queueing network is highly intractable. Therefore, an innovative approximation method, using jump-over blocking is proposed to accurately assess key performance statistics such as throughput and recirculation. Multi-class jump-over networks admit a product-form stationary distribution, and can be efficiently evaluated by Mean Value Analysis (MVA) and use of Norton's theorem. The method is most suitable to support rapid and optimal design of complex zone picking systems, in terms of number of segments, number and length of zones, buffer capacities, and storage allocation of products to zones, in order to meet prespecified performance targets. Comparison of the approximation results to simulation show that for a wide range of parameters the mean relative error in the system throughput is typically less than 1%. The approximation is also applied to evaluate a real-life zone picking system of a large wholesaler supplying non-food items.
Electronic Notes in Theoretical Computer Science, 2005
We consider a ∞uid ∞ow model processing two types of ∞uid at constant rate, where one type of ∞ui... more We consider a ∞uid ∞ow model processing two types of ∞uid at constant rate, where one type of ∞uid receives full service priority over the other. The two types of ∞uid are stored in separate inflnite capacity bufiers. The input is governed by an external Markovian environment process. We derive the Laplace-Stieltjes transform of the steady- state joint bufier content
DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
In this paper, we present a capacity analysis of an automated transportation system in a flexible... more In this paper, we present a capacity analysis of an automated transportation system in a flexible assembly factory. The transportation system, together with the workstations, is modeled as a network of queues with multiple job classes. Due to its complex nature, the steady-state behavior of this network is not described by a product-form solution. Therefore, we present an approximate method to determine the capacity of the network. We first study a number of key elements of the system separately and subsequently combine the results of this analysis in an Approximate Mean Value Analysis (AMVA) algorithm. The key elements are a buffer/transfer system (the bottleneck of the system), modeled as a preemptive-repeat priority queue with identical deterministic service times for the different job classes, a set of elevators, modeled as vacation servers, a number of work cells, modeled as multi-server queues, and several non-accumulating conveyor belts, modeled as ample servers. The AMVA alg...
This paper deals with the fixed-cycle traffic-light (FCTL) queue, where vehicles arrive at an int... more This paper deals with the fixed-cycle traffic-light (FCTL) queue, where vehicles arrive at an intersection controlled by a traffic light and form a queue. The traffic light alternates between green and red periods, and delayed vehicles are assumed to depart during the green period at equal time intervals. The key performance characteristic in the FCTL queue is the so-called mean overflow, defined as the mean queue length at the end of a green period. An exact solution for the mean overflow is available, but it has been considered to be of little practical value because it requires some numerical procedures. Therefore, most of the literature on the FCTL queue is about deriving approximations for the mean overflow. In deriving these approximations, most authors first approximate the FCTL queue by a bulk-service queue, approximate the mean overflow in the bulk-service queue, and use this as an approximation for the mean overflow in the FCTL queue. So far no quantitative comparison of b...
In this paper we study a general stochastic fluid model with a single infinite capacity buffer, w... more In this paper we study a general stochastic fluid model with a single infinite capacity buffer, where the buffer content can change continuously as well as by instantaneous upward jumps. The continuous as well as the instantaneous change is modulated by an external environment process modelled as a finite state continuous time Markov chain. The Laplace-Stieltjes transform of the steady-state joint distribution of the buffer content and the state of the environment is determined explicitly in terms of the solutions of a generalized eigenvalue problem. The methodology is illustrated by several well-known queueing problems.
We consider a firm which targets a certain level of customer responsiveness with a minimum operat... more We consider a firm which targets a certain level of customer responsiveness with a minimum operational cost. The firm employs a preorder strategy, in which customers place their orders before their actual need based on a predefined time window called commitment lead time and, in turn, they receive a bonus. The firm aims to determine the optimal control policy, which consists of the optimal commitment lead time and the optimal base-stock level, such that the total operational cost is minimized subject to a time-based service level target. We formulate two time-based service criteria to measure the firm's responsiveness in terms of average customer waiting time and individual customer waiting time in two constraint optimization models called ACO and CCO, respectively. We derive the exact probability distribution of customer waiting time, and we propose exact and heuristic optimization algorithms to solve the ACO and CCO models. We show that the commitment lead time not only increases the firm's responsiveness level but also decreases the customers' maximum waiting time. We find that when the firm targets a high level of responsiveness, the value of commitment lead time is more highlighted. We study multiple interesting extensions with two customer classes, random replenishment lead times and a combined model with two time-based service level targets.
European Journal of Operational Research, Apr 1, 2021
Many intra-logistics systems, such as automated container terminals, distribution warehouses, and... more Many intra-logistics systems, such as automated container terminals, distribution warehouses, and crossdocks, observe parallel process flows, which involve simultaneous (parallel) operations of independent resources while processing a job. When independent resources work simultaneously to process a common job, the effective service requirement of the job is difficult to estimate. For modeling simplicity, researchers tend to assume sequential operations of the resources. In this paper, we propose an efficient modeling approach for parallel process flows using two-phase servers. We develop a closed queuing network model to estimate system performance measures. Existing solution methods can evaluate the performance of closed queuing networks that consist of two-phase servers with exponential service times only. To solve closed queuing networks with general two-phase servers, we propose new solution methods: an approximate mean value analysis and a network aggregation dis-aggregation approach. We derive insights on the accuracy of the solution methods from numerical experiments. Although both solution methods are quite accurate in estimating performance measures, the network aggregation disaggregation approach consistently performs best. We illustrate the proposed modeling approach for two intra-logistic systems: a container terminal with automated guided vehicles and a shuttle-based compact storage system. Results show that approximating the simultaneous operations as sequential operations underestimates the container terminal throughput on average by 28% and at maximum up to 47%. Similarly, considering sequential operations of the resources in the compact storage system results in an underestimation of the throughput capacity up to 9%.
We study a multi-location inventory problem with a so-called quick response warehouse. In case of... more We study a multi-location inventory problem with a so-called quick response warehouse. In case of a stock-out at a local warehouse, the demand might be satisfied by a stock transfer from the quick response warehouse. We derive the optimal policy for when to accept and when to reject such a demand at the quick response warehouse. We also derive conditions under which it is always optimal to accept these demands. Furthermore, we conduct a numerical study and consider model variations.
The Medium Access Control (MAC) scheme proposed by DAVIC/DVB, IEEE 802.14 and DOCSIS for the upst... more The Medium Access Control (MAC) scheme proposed by DAVIC/DVB, IEEE 802.14 and DOCSIS for the upstream channel of Hybrid Fiber Coaxial (HFC) access networks is based on a mixable contention-based/contention-less time slot assignment. Contention-less slots are assigned by the head end to end stations according to a reservation scheme. Contentionbased slots are randomly accessed by active terminals without any preliminary allocation, so that collisions may occur. To resolve contention, the contention tree algorithm has been widely accepted by the DVB/DAVIC, IEEE 802.14 and DOCSIS standards for MAC because of higher throughput and lower access delay. In this paper we propose a novel contention resolution mechanism and compare its performance with that of existing procedures. The proposed procedure is termed as static arrival slot mechanism. In this mechanism, one slot in each frame is exclusively reserved for new arrivals that wish to access the channel using contention resolution, and at least one slot is reserved for resolving their contention if there was one in the arrival slot. The performance of the proposed mechanism is evaluated through analysis and simulation. The results show that the proposed mechanism outperforms existing contention resolution procedures under heavy traffic.
In this paper, we present and analyze a mathematical model for the computation of the system avai... more In this paper, we present and analyze a mathematical model for the computation of the system availability for a system of parallel machines with redundancies and repair priorities. Using the presented models, we show that the repair priorities have a strong effect on the performance of the system.
Proceedings Title: Proceedings of the 2012 Winter Simulation Conference (WSC), 2012
Magnetic Resonance Imaging (MRI) requires expensive diagnostic equipment and is labor intensive. ... more Magnetic Resonance Imaging (MRI) requires expensive diagnostic equipment and is labor intensive. To evaluate the effective use of the MRI resources a curve of flow time versus throughput may be helpful in quantifying the trade-off between patient waiting time and resource utilization, and in providing insight into operational time losses and variability. This curve may be obtained by simulation. However, building a detailed simulation model of an MRI department requires expertise typically unavailable in hospitals. To overcome this difficulty, we seek for an appropriate aggregate model of the MRI department, either a simulation or an analytical model. The aggregate model parameters are to be determined from hospital patient arrival and departure times. We study three different aggregate models for use in the MRI setting. To be able to evaluate the prediction accuracy of the candidate aggregate models we use a detailed simulation model as virtual MRI department.
Cardiothoracic surgery planning involves different resources such as operating theatre time, beds... more Cardiothoracic surgery planning involves different resources such as operating theatre time, beds, IC beds and nursing staff. In practice the planning in the Thorax Centre focuses on optimal use of operating theatre time, though the performance of the Thorax Centre as a whole is often more limited by the capacity of the IC. For operating theatres a master surgical schedule is used to allocate operating theatre resources at tactical level for a longer period. Operational schedules at weekly level are derived from this master schedule. Within cardiothoracic surgery different categories of patients can be distinguished on behalf of their requirement of resources. The mix of patients is, therefore, an important decision variable for the Thorax Centre to manage the use of these resources. In the paper we will consider the planning problem to generate a master operation schedule that realises a given target of patient throughput and optimises an object function for the utilisation of resources. This problem can be mathematically approached by mixed integer programming. We will discuss the mathematical model developed for this planning problem, the implementation in a decision support model for tactical surgery planning, the results obtained and the way the model can help to broaden the focus of planning of cardiothoracic patients.
DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428), 2003
The Medium Access Control (MAC) scheme proposed by DAVIC/DVB, IEEE 802.14 and DOCSIS for the upst... more The Medium Access Control (MAC) scheme proposed by DAVIC/DVB, IEEE 802.14 and DOCSIS for the upstream channel of Hybrid Fiber Coaxial (HFC) access networks is based on a mixable contention-based/contention-less time slot assignment. Contention-less slots are assigned by the head end to end stations according to a reservation scheme. Contentionbased slots are randomly accessed by active terminals without any preliminary allocation, so that collisions may occur. To resolve contention, the contention tree algorithm has been widely accepted by the DVB/DAVIC, IEEE 802.14 and DOCSIS standards for MAC because of higher throughput and lower access delay. In this paper we propose a novel contention resolution mechanism and compare its performance with that of existing procedures. The proposed procedure is termed as static arrival slot mechanism. In this mechanism, one slot in each frame is exclusively reserved for new arrivals that wish to access the channel using contention resolution, and at least one slot is reserved for resolving their contention if there was one in the arrival slot. The performance of the proposed mechanism is evaluated through analysis and simulation. The results show that the proposed mechanism outperforms existing contention resolution procedures under heavy traffic.
This paper develops an analytical model of sequential zone picking systems. The systems belong to... more This paper develops an analytical model of sequential zone picking systems. The systems belong to the most popular internal transport and order picking systems in practice, due to their scalability, flexibility, highthroughput ability, and fit-for-use for a wide range of products and order profiles. The major disadvantage of such systems, though, is congestion and blocking under heavy use, leading to long order lead times. In order to diminish blocking and congestion most systems make use of a dynamic block-and-recirculate protocol. The various elements of the system, like conveyor lanes and the pick zones, are modeled as a network of queues with multiple order classes and with capacity constraints on subnetworks, including the dynamic block-and-recirculate protocol. Due to this protocol, however, the stationary distribution of the queueing network is highly intractable. Therefore, an innovative approximation method, using jump-over blocking is proposed to accurately assess key performance statistics such as throughput and recirculation. Multi-class jump-over networks admit a product-form stationary distribution, and can be efficiently evaluated by Mean Value Analysis (MVA) and use of Norton's theorem. The method is most suitable to support rapid and optimal design of complex zone picking systems, in terms of number of segments, number and length of zones, buffer capacities, and storage allocation of products to zones, in order to meet prespecified performance targets. Comparison of the approximation results to simulation show that for a wide range of parameters the mean relative error in the system throughput is typically less than 1%. The approximation is also applied to evaluate a real-life zone picking system of a large wholesaler supplying non-food items.
Electronic Notes in Theoretical Computer Science, 2005
We consider a ∞uid ∞ow model processing two types of ∞uid at constant rate, where one type of ∞ui... more We consider a ∞uid ∞ow model processing two types of ∞uid at constant rate, where one type of ∞uid receives full service priority over the other. The two types of ∞uid are stored in separate inflnite capacity bufiers. The input is governed by an external Markovian environment process. We derive the Laplace-Stieltjes transform of the steady- state joint bufier content
DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
In this paper, we present a capacity analysis of an automated transportation system in a flexible... more In this paper, we present a capacity analysis of an automated transportation system in a flexible assembly factory. The transportation system, together with the workstations, is modeled as a network of queues with multiple job classes. Due to its complex nature, the steady-state behavior of this network is not described by a product-form solution. Therefore, we present an approximate method to determine the capacity of the network. We first study a number of key elements of the system separately and subsequently combine the results of this analysis in an Approximate Mean Value Analysis (AMVA) algorithm. The key elements are a buffer/transfer system (the bottleneck of the system), modeled as a preemptive-repeat priority queue with identical deterministic service times for the different job classes, a set of elevators, modeled as vacation servers, a number of work cells, modeled as multi-server queues, and several non-accumulating conveyor belts, modeled as ample servers. The AMVA alg...
This paper deals with the fixed-cycle traffic-light (FCTL) queue, where vehicles arrive at an int... more This paper deals with the fixed-cycle traffic-light (FCTL) queue, where vehicles arrive at an intersection controlled by a traffic light and form a queue. The traffic light alternates between green and red periods, and delayed vehicles are assumed to depart during the green period at equal time intervals. The key performance characteristic in the FCTL queue is the so-called mean overflow, defined as the mean queue length at the end of a green period. An exact solution for the mean overflow is available, but it has been considered to be of little practical value because it requires some numerical procedures. Therefore, most of the literature on the FCTL queue is about deriving approximations for the mean overflow. In deriving these approximations, most authors first approximate the FCTL queue by a bulk-service queue, approximate the mean overflow in the bulk-service queue, and use this as an approximation for the mean overflow in the FCTL queue. So far no quantitative comparison of b...
In this paper we study a general stochastic fluid model with a single infinite capacity buffer, w... more In this paper we study a general stochastic fluid model with a single infinite capacity buffer, where the buffer content can change continuously as well as by instantaneous upward jumps. The continuous as well as the instantaneous change is modulated by an external environment process modelled as a finite state continuous time Markov chain. The Laplace-Stieltjes transform of the steady-state joint distribution of the buffer content and the state of the environment is determined explicitly in terms of the solutions of a generalized eigenvalue problem. The methodology is illustrated by several well-known queueing problems.
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Papers by Ivo Adan