scholarly journals Analysis of semi-open queueing networks using lost customers approximation with an application to robotic mobile fulfilment systems

OR Spectrum ◽  
2021 ◽  
Author(s):  
Sonja Otten ◽  
Ruslan Krenzler ◽  
Lin Xie ◽  
Hans Daduna ◽  
Karsten Kruse
Keyword(s):  
Queueing Networks ◽  
Queueing Network ◽  
Arrival Rate ◽  
Second Step ◽  
Original Network ◽  
Theoretical Methods ◽  
Solution Approach ◽  
Open Queueing Networks ◽  
Open Queueing Network ◽  
Storage Area

AbstractWe consider a semi-open queueing network (SOQN), where one resource from a resource pool is needed to serve a customer. If on arrival of a customer some resource is available, the resource is forwarded to an inner network to complete the customer’s order. If no resource is available, the new customer waits in an external queue until one becomes available (“backordering”). When a resource exits the inner network, it is returned to the resource pool. We develop a new solution approach. In a first step we modify the system such that new arrivals are lost if the resource pool is empty (“lost customers”). We adjust the arrival rate of the modified system such that the throughputs in all nodes of the inner network are pairwise identical to those in the original network. Using queueing theoretical methods, in a second step we reduce this inner network to a two-station system including the resource pool. For this two-station systems, we invert the first step and obtain a standard SOQN which can be solved analytically. We apply our results to storage and delivering systems with robotic mobile fulfilment systems (RMFSs). Instead of sending pickers to the storage area to search for the ordered items and pick them, robots carry shelves with ordered items from the storage area to picking stations. We model the RMFS as an SOQN to determine the minimal number of robots.

scholarly journals Modeling and performance analysis of shuttle-based compact storage systems under parallel processing policy

PLoS ONE ◽  
2021 ◽  
Vol 16 (11) ◽  
pp. e0259773
Author(s):  
Lei Deng ◽  
Lei Chen ◽  
Jingjie Zhao ◽  
Ruimei Wang
Keyword(s):  
Parallel Processing ◽  
Storage Systems ◽  
Current System ◽  
Queueing Network ◽  
Arrival Rate ◽  
Width Ratio ◽  
Storage And Retrieval ◽  
Sequential Processing ◽  
Open Queueing Network ◽  
And Performance

Short response time for order processing is important for modern warehouses, which can be potentially achieved by adopting appropriate processing policy. The parallel processing policy have advantages in improving performance of many autonomous storage and retrieval systems. However, researchers tend to assume a sequential processing policy managing the movement of independent resources in shuttle-based compact storage systems. This paper models and analyses a single-tier of specialized shuttle-based compact storage systems under parallel processing policy. The system is modeled as a semi-open queueing network with class switching and the parallel movement of shuttles and the transfer car is modeled using a fork-join queueing network. The analytical model is validated against simulations and the results show our model can accurately estimate the system performance. Numerical experiments and a real case are carried out to compare the performance of parallel and sequential processing policies. The results suggest a critical transaction arrival rate and depth/width ratio, below which the sequential processing policy outperforms the parallel processing policy. However, the advantage of sequential processing policy is decreasing with the increasing of shuttle number, transaction arrival rate and depth/width ratio. The results also suggest an optimal depth/width ratio with a value of 1.75 for minimizing the expected throughput time in the real system. Given the current system configurations, the parallel processing policy should be considered when the number of shuttles is larger than 2 or the transaction arrival rate is larger than 24 per hour.

STABILIZING PERFORMANCE IN NETWORKS OF QUEUES WITH TIME-VARYING ARRIVAL RATES

2014 ◽  
Vol 28 (4) ◽  
pp. 419-449 ◽  
Author(s):  
Yunan Liu ◽  
Ward Whitt
Keyword(s):  
Quality Of Service ◽  
Limit Theorem ◽  
Queueing Networks ◽  
Queueing Network ◽  
Arrival Rate ◽  
Time Varying ◽  
Departure Process ◽  
Feed Forward ◽  
Wide Range

This paper investigates extensions to feed-forward queueing networks of an algorithm to set staffing levels (the number of servers) to stabilize performance % at Quality of Service (QoS) targets in anMt/GI/st+GImulti-server queue with a time-varying arrival rate. The model has a non-homogeneous Poisson process (NHPP), customer abandonment, and non-exponential service and patience distributions. For a single queue, simulation experiments showed that the algorithm successfully stabilizes abandonment probabilities and expected delays over a wide range of Quality-of-Service (QoS) targets. A limit theorem showed that stable performance at fixed QoS targets is achieved asymptotically as the scale increases (by letting the arrival rate grow while holding the service and patience distributions fixed). Here we extend that limit theorem to a feed-forward queueing network. However, these fixed QoS targets provide low QoS as the scale increases. Hence, these limits primarily support the algorithm with a low QoS target. For a high QoS target, effectiveness depends on the NHPP property, but the departure process never is exactly an NHPP. Thus, we investigate when a departure process can be regarded as approximately an NHPP. We show that index of dispersion for counts is effective for determining when a departure process is approximately an NHPP in this setting. In the important common case when all queues have high QoS targets, we show that both: (i) the departure process is approximately an NHPP from this perspective and (ii) the algorithm is effective.

Solving Open Queueing Network Problem

2018 ◽  
Vol 6 (7) ◽  
pp. 116
Author(s):  
Aman Kumar Sinha ◽  
S. P. Varma
Keyword(s):  
Queueing Networks ◽  
Queueing Network ◽  
Service Facility ◽  
Network Problem ◽  
Open Queueing Network

Queueing networks may be considered as a group of inter-connected nodes (say ) where each node represents a service facility of some kind with servers at the node ( ). We propose to apply 1st the method given by J. R. Jackson and then we would like to solve the same problem by the method of J. D. C. Little.

scholarly journals ANALISIS PERFORMANSI SERVER SISTEM INFORMASI AKADEMIK UNIVERSITAS MERCU BUANA DENGAN OPEN QUEUEING NETWORK

2015 ◽  
Vol 7 (2) ◽  
pp. 244
Author(s):  
Desi Ramayanti
Keyword(s):  
Service Time ◽  
Queueing Network ◽  
Arrival Rate ◽  
Service Demand ◽  
Open Queueing Network ◽  
Data Error ◽  
Resource Service ◽  
Time Resource

SIA (Sistem Informasi Akademik) merupakan sebuah sistem informasi penting yang berkaitan dengan nilai yang sudah diperoleh untuk setiap matakuliah yang telah diambil, status dari mahasiswa pada semester terkait, dll. SIA ini akan selalu diakses oleh mahasiswa dan juga dosen di lingkungan UMB, baik pada setiap awal semester, pertengahan semester atau pada akhir semester. SIA merupakan fitur  penting yang harus tetap available setiap saat, dan mampu melayani ribuan user dengan baik. Keterlambatan data (delay), kehilangan data (lost) dan kerusakan data (error), harus menjadi point penting dalam sebuah system, karena jika ketiga hal tersebut terjadi, maka nilai informasi akan berkurang atau menjadi tidak berarti lagi, dan hal ini akan sangat merugikan, khususnya kepada mahasiswa sebagai konsumen yang wajib mendapatkan pelayanan terbaik. Maka dikarenakan hal tersebut, maka penulis melakukan penelitian berkaitan dengan performansi SIA saat ini. Dalam penelitian ini, penulis melakukan analisis performansi SIA yang terkait dengan arrival rate resource, service time resource utilisasi resource, Rata-rata jumlah kunjungan ke resource, service demand resourcedan arrival rate maksimum dari server. Dari hasil analisis maka diperoleh kesimpulan bahwa performansi dari server SIA yang ada saat ini kurang maksimum dengan jumlah mahasiswa yang ada. Server Sistem Informasi Akademik saat ini hanya mampu melayani request per detik sebanyak 7.278 request. Sedangkan arrival rate yang ada yaitu 8.88 request per detik, sehingga kemungkinan lost request adalah 21.98%.

scholarly journals Finite Queueing Modeling and Optimization: A Selected Review

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
F. R. B. Cruz ◽  
T. van Woensel
Keyword(s):  
Performance Evaluation ◽  
Queueing Networks ◽  
Queueing Network ◽  
Expansion Method ◽  
Network Analyzer ◽  
Modeling And Optimization ◽  
Product Engineering ◽  
Service Rates

This review provides an overview of the queueing modeling issues and the related performance evaluation and optimization approaches framed in a joined manufacturing and product engineering. Such networks are represented as queueing networks. The performance of the queueing networks is evaluated using an advanced queueing network analyzer: the generalized expansion method. Secondly, different model approaches are described and optimized with regard to the key parameters in the network (e.g., buffer and server sizes, service rates, and so on).

Software for Queueing Analysis

2018 ◽  
pp. 255-291
Keyword(s):  
Queueing Networks ◽  
Discrete Event ◽  
Queueing Network ◽  
Queueing Analysis ◽  
Discrete Events ◽  
Technical Literature ◽  
Event Simulation ◽  
Statistical Program ◽  
Service Times ◽  
Waiting Lines

Chapter 8 gives a brief discussion of computer simulation for discrete events. The chapter lists software programs in the technical literature that outline programs for the simulation of discrete events, both of commercial origin and free programs. In addition to the lists submitted, the authors present specialized packages for analysis and simulation of waiting lines in the R language. Statistical considerations are presented, which must be taken into account when obtaining data from simulations in situations of waiting lines. Chapter 8 presents three packages of the statistical program R: the “queueing” analysis package provides versatile tools for analysis of birth- and death-based Markovian queueing models and single and multiclass product-form queueing networks; “simmer” package is a process-oriented and trajectory-based discrete-event simulation (DES) package for R; and, the purpose of the “queuecomputer” package is to calculate, deterministically, the outputs of a queueing network, given the arrival and service times of all the customers. It also uses simulation for the implementation of a method for the calculation of queues with arbitrary arrival and service times. For each theme, the authors show the use of the packages in R.

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