11th EAI International Conference on Performance Evaluation Methodologies and Tools

Research Article

FCFS Parallel Service Systems and Matching Models

  • @INPROCEEDINGS{10.4108/eai.5-12-2017.2274205,
        author={Ivo  Adan and Rhonda  Righter and Gideon  Weiss},
        title={FCFS Parallel Service Systems and Matching Models},
        proceedings={11th EAI International Conference on Performance Evaluation Methodologies and Tools},
        publisher={ACM},
        proceedings_a={VALUETOOLS},
        year={2018},
        month={8},
        keywords={parallel service; fcfs; redundancy service; matching},
        doi={10.4108/eai.5-12-2017.2274205}
    }
    
  • Ivo Adan
    Rhonda Righter
    Gideon Weiss
    Year: 2018
    FCFS Parallel Service Systems and Matching Models
    VALUETOOLS
    ACM
    DOI: 10.4108/eai.5-12-2017.2274205
Ivo Adan1, Rhonda Righter2, Gideon Weiss3,*
  • 1: Eindhoven University of Technology
  • 2: University of California at Berkeley
  • 3: The University of Haifa
*Contact email: gweiss@stat.haifa.ac.il

Abstract

We consider parallel service models in which customers of several types are served by several types of servers subject to a bipartite compatibility graph, and the service policy is first come first served. Two of the models have a fixed set of servers. The first is a queueing model in which arriving customers are assigned to the longest idling compatible server if available, or else queue up in a single queue, and servers that become available pick the longest waiting compatible customer, as studied by Adan and Weiss, 2014. The second is a redundancy service model where arriving customers split into copies that queue up at all the compatible servers, and are served in each queue on FCFS basis, and leave the system when the first copy completes service, as studied by Gardner et al., 2016. The third model is a matching queueing model with a random stream of arriving servers. Arriving customers queue in a single queue and arriving servers match with the first compatible customer and leave the system at the moment of arrival, or they leave without a customer. The last model is relevant to organ transplants, to housing assignments, to adoptions and many other situations.

We study the relations between these models, and show that they are closely related to the FCFS infinite bipartite matching model, in which two infinite sequences of customers and servers of several types are matched FCFS according to a bipartite compatibility graph, as studied by Busic et al., 2017.